| Number | Orbifold | Embedding | Normal | Subgroup index | Curvature | P spacegroup | G spacegroup | D spacegroup | Utiling count | Conjugacy class size | Generators | Maximal subgroups |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | ooo | Y | 96 | -4 | P1 | P1 | P1 | 0 | 1 | [ ] | ||
| 2 | 22222222 | Y | 48 | -2 | P-1 | P-1 | P-1 | 0 | 1 | [ r3*r1*r3*r1*r3*r1 ] | 1 | |
| 3 | xxxx | c | Y | 48 | -2 | P-1 | P1 | P1 | 0 | 1 | [ r1*r2*r3*r2*r3*r1*r3*r2*r3 ] | 1 |
| 4 | xxxx | b | Y | 48 | -2 | P1 | P1 | P-1 | 0 | 1 | [ r1*r2*r3*r1*r2*r3*r2*r1*r3 ] | 1 |
| 5 | xxxx | a | N | 48 | -2 | P21 | P1 | Cc | 0 | 3 | [ r1*r2*r3*r1*r3*r1*r3 ] | 1 |
| 6 | o** | N | 48 | -2 | Pm | P1 | C2 | 0 | 3 | [ r2 ] | 1 | |
| 7 | o2222 | b | N | 48 | -2 | P2 | C2 | C2 | 0 | 3 | [ r3*r2*r3*r2 ] | 1 |
| 8 | oo | b | N | 48 | -2 | Pc | Cc | Cc | 0 | 3 | [ r2*r3*r1*r3*r2*r1*r3*r1 ] | 1 |
| 9 | **xx | b | N | 48 | -2 | Cm | P1 | C2 | 0 | 6 | [ r1 ] | 1 |
| 10 | **xx | a | N | 48 | -2 | C2 | P1 | Cm | 0 | 6 | [ r3 ] | 1 |
| 11 | o2222 | a | N | 48 | -2 | C2 | C2 | C2 | 0 | 6 | [ r2*r1 ] | 1 |
| 12 | oo | a | N | 48 | -2 | Cc | Cc | Cc | 0 | 6 | [ r3*r1*r3*r1*r3*r2 ] | 1 |
| 13 | o33 | N | 32 | -4/3 | R3 | R3 | R3 | 0 | 4 | [ r3*r1*r3*r1 ] | 1 | |
| 14 | 222222 | d | Y | 24 | -1 | P222 | I212121 | F222 | 0 | 1 | [ r3*r2*r3*r2, r1*r3*r2*r3*r2*r1 ] | 7 |
| 15 | 2222x | Y | 24 | -1 | P-1 | P-1 | P-1 | 0 | 1 | [ r3*r1*r3*r1*r3*r1, r1*r2*r3*r1*r2*r3*r2*r1*r3 ] | 2.3.4. | |
| 16 | 222222 | c | N | 24 | -1 | C222 | F222 | I212121 | 0 | 3 | [ r2*r1, r3*r1*r3*r2*r3*r2*r1*r3 ] | 11.7. |
| 17 | 4444 | N | 24 | -1 | P-4 | I-4 | I-4 | 0 | 3 | [ r3*r2 ] | 7 | |
| 18 | o22 | d | N | 24 | -1 | P4 | I41 | I41 | 0 | 3 | [ r3*r2*r3*r2, r1*r3*r1*r3*r2*r1 ] | 7 |
| 19 | 22xx | d | N | 24 | -1 | P-4 | C2 | I41 | 0 | 3 | [ r3*r2*r3*r2, r1*r2*r3*r1*r2*r3*r1 ] | 7 |
| 20 | 22** | b | N | 24 | -1 | Cmm2 | C2 | I212121 | 0 | 3 | [ r1, r3*r1*r3*r2*r3*r2*r1*r3 ] | 9.7. |
| 21 | o22 | c | N | 24 | -1 | Ccc2 | Fdd2 | Iba2 | 0 | 3 | [ r3*r2*r3*r2, r3*r1*r3*r2*r3*r1 ] | 12.7. |
| 22 | 22** | a | N | 24 | -1 | P2/m | C2 | P2 | 0 | 3 | [ r2, r3*r1*r3*r2*r3*r2*r1*r3 ] | 3.6.7. |
| 23 | 2222* | N | 24 | -1 | P21/m | P-1 | C2/c | 0 | 3 | [ r2, r3*r1*r3*r1*r3*r1 ] | 2.5.6. | |
| 24 | o22 | b | N | 24 | -1 | Pnn2 | Iba2 | Fdd2 | 0 | 3 | [ r3*r2*r3*r2, r2*r3*r1*r3*r2*r1*r3*r1 ] | 8.7. |
| 25 | *22*22 | b | N | 24 | -1 | Pmm2 | C2 | F222 | 0 | 3 | [ r2, r3*r2*r3 ] | 6.7. |
| 26 | 22xx | c | N | 24 | -1 | P42 | C2 | I-4 | 0 | 3 | [ r3*r2*r3*r2, r1*r2*r3*r2*r3*r1*r3 ] | 7 |
| 27 | 222222 | b | N | 24 | -1 | P2/c | C2/c | C2/c | 0 | 3 | [ r3*r2*r3*r2, r3*r1*r3*r1*r3*r1 ] | 8.2.7. |
| 28 | *22*22 | a | N | 24 | -1 | C222 | C2 | Imm2 | 0 | 3 | [ r3, r2*r3*r2 ] | 10.7. |
| 29 | 22xx | b | N | 24 | -1 | P21212 | C2 | Fdd2 | 0 | 3 | [ r3*r2*r3*r2, r1*r2*r3*r1*r3*r1*r3 ] | 5.7. |
| 30 | o* | N | 24 | -1 | Cm | Cc | C2/c | 0 | 3 | [ r2, r3*r1*r2*r3*r2*r1*r3*r1 ] | 8.4.6. | |
| 31 | xxx | N | 24 | -1 | P21/c | Cc | Pc | 0 | 3 | [ r1*r2*r3*r1*r3*r1*r3, r3*r1*r2*r3*r2*r1*r3*r1 ] | 8.3.5. | |
| 32 | 22xx | a | N | 24 | -1 | C2 | C2 | C2/c | 0 | 3 | [ r3*r2*r3*r2, r1*r3*r1*r2*r3*r1*r3 ] | 4.5.7. |
| 33 | **x | b | N | 24 | -1 | Cmc21 | Cc | Iba2 | 0 | 6 | [ r1, r3*r1*r3*r1*r3*r2 ] | 12.9.5. |
| 34 | *2222x | N | 24 | -1 | Amm2 | C2 | I222 | 0 | 6 | [ r1, r2 ] | 9.11.6. | |
| 35 | 22*x | c | N | 24 | -1 | C2221 | C2 | Ima2 | 0 | 6 | [ r2*r1, r3*r1*r3*r1*r3 ] | 10.11.5. |
| 36 | 22*2222 | N | 24 | -1 | C2/m | P-1 | C2/m | 0 | 6 | [ r1, r3*r1*r3*r1*r3 ] | 9.10.2. | |
| 37 | 22*x | b | N | 24 | -1 | C2/m | C2 | C2 | 0 | 6 | [ r1, r3*r2*r3*r1*r3*r2*r3*r2 ] | 9.11.3. |
| 38 | *** | N | 24 | -1 | Abm2 | Cc | Ima2 | 0 | 6 | [ r1, r3*r1*r2*r3*r2*r1*r3 ] | 8.9.10. | |
| 39 | **x | a | N | 24 | -1 | Ama2 | Cc | Ima2 | 0 | 6 | [ r2, r3*r1*r3*r1*r3 ] | 12.10.6. |
| 40 | *xx | c | N | 24 | -1 | Cm | Cc | C2/c | 0 | 6 | [ r1, r3*r1*r2*r3*r2*r1*r3*r2 ] | 12.9.4. |
| 41 | *xx | b | N | 24 | -1 | Pmn21 | Cc | Fdd2 | 0 | 6 | [ r2, r1*r3*r1*r2*r3*r1*r3 ] | 8.5.6. |
| 42 | 22*x | a | N | 24 | -1 | C2 | C2 | C2/m | 0 | 6 | [ r2*r1, r3*r1*r2*r3*r2*r1*r3 ] | 10.11.4. |
| 43 | o22 | a | N | 24 | -1 | Aba2 | Fdd2 | Iba2 | 0 | 6 | [ r2*r1, r3*r1*r2*r3*r2*r1*r3*r1 ] | 12.8.11. |
| 44 | 222222 | a | N | 24 | -1 | C2/c | C2/c | C2/c | 0 | 6 | [ r2*r1, r3*r1*r3*r1*r3*r1 ] | 12.2.11. |
| 45 | *xx | a | N | 24 | -1 | C2/c | Cc | Cm | 0 | 6 | [ r3, r2*r3*r1*r2*r3*r2*r3*r1 ] | 12.10.3. |
| 46 | 3xx | b | N | 16 | -2/3 | R-3 | R3 | R3 | 0 | 4 | [ r3*r1*r3*r1, r1*r2*r3*r1*r2*r3*r2 ] | 13.3. |
| 47 | *3*3 | b | N | 16 | -2/3 | Fdd2 | R3 | R32 | 0 | 4 | [ r1, r3*r1*r3 ] | 13.9. |
| 48 | *3*3 | a | N | 16 | -2/3 | R32 | R3 | R3m | 0 | 4 | [ r3, r1*r3*r1 ] | 13.10. |
| 49 | 22223 | N | 16 | -2/3 | R32 | R32 | R32 | 0 | 4 | [ r3*r1*r3*r1, r2*r3*r2*r1*r3*r2 ] | 13.11. | |
| 50 | 2266 | N | 16 | -2/3 | R-3 | R-3 | R-3 | 0 | 4 | [ r3*r1 ] | 13.2. | |
| 51 | o3 | N | 16 | -2/3 | R3c | R3c | R3c | 0 | 4 | [ r3*r1*r3*r1, r2*r3*r1*r2*r3*r2*r3*r1 ] | 12.13. | |
| 52 | 3xx | a | N | 16 | -2/3 | R3 | R3 | R-3 | 0 | 4 | [ r3*r1*r3*r1, r2*r3*r1*r2*r3*r2*r3 ] | 13.4. |
| 53 | 222x | c | Y | 12 | -1/2 | I222 | I212121 | Fddd | 0 | 1 | [ r3*r2*r3*r2, r1*r3*r2*r3*r2*r1, r1*r2*r3*r1*r3*r1*r3 ] | 32.29.14. |
| 54 | 22222 | c | Y | 12 | -1/2 | Pnnn | Ibca | Fddd | 0 | 1 | [ r3*r2*r3*r2, r1*r3*r2*r3*r2*r1, r3*r1*r3*r1*r3*r1 ] | 27.14.24. |
| 55 | *222222 | b | Y | 12 | -1/2 | Pmmm | I212121 | P222 | 327 | 1 | [ r2, r3*r2*r3, r1*r3*r2*r3*r1 ] | 22.14.25. |
| 56 | 2xx | b | N | 12 | -1/2 | I4 | I41 | I41/a | 0 | 3 | [ r3*r2*r3*r2, r1*r3*r1*r3*r2*r1, r1*r2*r3*r2*r3*r1*r3 ] | 32.26.18. |
| 57 | 2*2222 | b | N | 12 | -1/2 | Cmmm | F222 | C222 | 0 | 3 | [ r1, r2, r3*r1*r3*r2*r3*r2*r1*r3 ] | 22.16.20.34.37. |
| 58 | 222x | b | N | 12 | -1/2 | P42/n | C2/c | I41/a | 0 | 3 | [ r3*r2*r3*r2, r3*r1*r3*r1*r3*r1, r1*r2*r3*r1*r2*r3*r1 ] | 19.27.26. |
| 59 | 2** | c | N | 12 | -1/2 | Fmm2 | Fdd2 | Ibca | 0 | 3 | [ r1, r3*r1*r3*r1*r3*r2, r3*r1*r2*r3*r2*r1*r3*r2 ] | 40.32.33.21.20. |
| 60 | **22 | c | N | 12 | -1/2 | P4mm | I41 | I4122 | 0 | 3 | [ r1, r3*r2*r3 ] | 18.20.25. |
| 61 | o2 | N | 12 | -1/2 | P4nc | I41cd | I41cd | 0 | 3 | [ r3*r2*r3*r2, r1*r3*r1*r3*r2*r1, r3*r1*r3*r2*r3*r1 ] | 21.18.24. | |
| 62 | 44* | b | N | 12 | -1/2 | P-421m | I-4 | I-42d | 0 | 3 | [ r1, r3*r1*r3*r2*r1*r3 ] | 29.20.17. |
| 63 | 2*x | b | N | 12 | -1/2 | P42nm | Iba2 | I-42d | 0 | 3 | [ r1, r2*r3*r1*r2*r3*r1*r3 ] | 20.26.24. |
| 64 | *4444 | N | 12 | -1/2 | P-4m2 | I-4 | I-4m2 | 211 | 3 | [ r2, r3 ] | 28.17.25. | |
| 65 | 222* | b | N | 12 | -1/2 | P-42m | I212121 | I4122 | 0 | 3 | [ r1, r3*r2*r3*r2 ] | 20.19.14. |
| 66 | 22*22 | e | N | 12 | -1/2 | P-4m2 | F222 | I4122 | 0 | 3 | [ r2, r3*r2*r3, r1*r3*r2*r1*r3*r1 ] | 19.16.25. |
| 67 | 22*22 | d | N | 12 | -1/2 | Pmmn | C2/c | Fddd | 0 | 3 | [ r2, r3*r2*r3, r3*r1*r3*r1*r3*r1 ] | 41.23.29.27.25. |
| 68 | *2*2 | b | N | 12 | -1/2 | P42mc | Fdd2 | I-4c2 | 0 | 3 | [ r2, r3*r2*r3, r3*r1*r3*r2*r3*r1 ] | 21.26.25. |
| 69 | *22x | b | N | 12 | -1/2 | Imm2 | Iba2 | Fddd | 0 | 3 | [ r2, r3*r2*r3, r1*r3*r1*r2*r3*r1*r3 ] | 41.30.32.25.24. |
| 70 | **22 | b | N | 12 | -1/2 | Cccm | Fdd2 | Cmm2 | 0 | 3 | [ r2, r3*r1*r3*r1*r3, r3*r1*r2*r3*r2*r1*r3 ] | 39.21.28.45.22. |
| 71 | 222* | a | N | 12 | -1/2 | C2/m | C2/c | P2/c | 0 | 3 | [ r2, r3*r1*r3*r1*r3*r1, r3*r1*r2*r3*r2*r1*r3*r1 ] | 15.23.22.30.31.32.27. |
| 72 | 2*x | a | N | 12 | -1/2 | Pnnm | Iba2 | Pnn2 | 0 | 3 | [ r2, r1*r3*r1*r2*r3*r1*r3, r1*r3*r1*r3*r2*r1*r3 ] | 41.31.29.22.24. |
| 73 | 2** | b | N | 12 | -1/2 | P4/m | I41 | P42 | 0 | 3 | [ r2, r3*r2*r3*r1 ] | 22.18.19. |
| 74 | 44* | a | N | 12 | -1/2 | P42/m | I-4 | P-4 | 0 | 3 | [ r2, r3*r1*r3*r2*r1*r3 ] | 22.26.17. |
| 75 | 22*22 | c | N | 12 | -1/2 | F222 | F222 | Imma | 0 | 3 | [ r2*r1, r3*r1*r3*r1*r3, r3*r1*r2*r3*r2*r1*r3 ] | 32.42.16.35.28. |
| 76 | 22222 | b | N | 12 | -1/2 | Ccca | Fddd | Ibca | 0 | 3 | [ r2*r1, r3*r1*r3*r1*r3*r1, r3*r1*r2*r3*r2*r1*r3*r1 ] | 21.16.43.27.44. |
| 77 | 22222 | a | N | 12 | -1/2 | P422 | I4122 | I4122 | 0 | 3 | [ r2*r1, r3*r2*r3*r1 ] | 18.16.14. |
| 78 | 2244 | c | N | 12 | -1/2 | P-4n2 | I-4c2 | I-42d | 0 | 3 | [ r2*r1, r3*r1*r3*r2*r1*r3 ] | 16.17.24. |
| 79 | 222x | a | N | 12 | -1/2 | P42212 | F222 | I-42d | 0 | 3 | [ r2*r1, r1*r3*r1*r2*r3*r1*r3 ] | 29.16.26. |
| 80 | *2*2 | a | N | 12 | -1/2 | P4212 | I41 | I41md | 0 | 3 | [ r3, r2*r3*r2, r1*r3*r1*r3*r2*r1 ] | 29.28.18. |
| 81 | 22*22 | b | N | 12 | -1/2 | P4222 | I212121 | I-4m2 | 0 | 3 | [ r3, r2*r3*r2, r1*r3*r2*r3*r2*r1 ] | 28.26.14. |
| 82 | *22x | a | N | 12 | -1/2 | P-4n2 | Iba2 | I41md | 0 | 3 | [ r3, r2*r3*r2, r1*r2*r3*r1*r2*r3*r1 ] | 28.19.24. |
| 83 | *222222 | a | N | 12 | -1/2 | Cmma | C2/c | Imma | 1026 | 3 | [ r1, r3*r1*r3*r1*r3, r3*r1*r2*r3*r2*r1*r3 ] | 38.20.28.27.36. |
| 84 | 44x | N | 12 | -1/2 | I-4 | I-4 | I41/a | 0 | 3 | [ r3*r2, r1*r2*r3*r1*r2*r3*r1 ] | 32.19.17. | |
| 85 | 2xx | a | N | 12 | -1/2 | P-421c | F222 | I41cd | 0 | 3 | [ r3*r2*r3*r2, r3*r1*r3*r2*r3*r1, r1*r2*r3*r1*r2*r3*r1 ] | 29.19.21. |
| 86 | 2244 | b | N | 12 | -1/2 | P-42c | I-42d | I-4c2 | 0 | 3 | [ r3*r2, r1*r3*r2*r3*r2*r1 ] | 21.17.14. |
| 87 | 2244 | a | N | 12 | -1/2 | P4/n | I41/a | I41/a | 0 | 3 | [ r3*r2, r1*r3*r1*r3*r2*r1 ] | 18.27.17. |
| 88 | 2** | a | N | 12 | -1/2 | Cmca | Fdd2 | Abm2 | 0 | 6 | [ r1, r3*r1*r3*r1*r3*r2, r3*r1*r2*r3*r2*r1*r3 ] | 43.45.38.31.33.35.37. |
| 89 | 22*22 | a | N | 12 | -1/2 | C2/m | C2/c | C2/m | 0 | 6 | [ r1, r3*r1*r3*r1*r3, r3*r1*r2*r3*r2*r1*r3*r2 ] | 15.40.42.45.44.36.37. |
| 90 | 2*2222 | a | N | 12 | -1/2 | Cmcm | C2/c | Ibam | 0 | 6 | [ r1, r2, r3*r1*r3*r1*r3 ] | 44.39.23.33.34.35.36. |
| 91 | **22 | a | N | 12 | -1/2 | Fmm2 | Fdd2 | Ibam | 0 | 6 | [ r1, r2, r3*r1*r2*r3*r2*r1*r3 ] | 40.43.42.38.39.30.34. |
| 92 | 2233 | Y | 8 | -1/3 | P23 | I213 | F23 | 0 | 1 | [ r3*r1*r3*r1, r3*r2*r3*r2 ] | 13.14. | |
| 93 | 2226 | N | 8 | -1/3 | R-3c | R-3c | R-3c | 0 | 4 | [ r3*r1, r2*r3*r2*r1*r3*r2 ] | 49.44.50.51. | |
| 94 | 26x | N | 8 | -1/3 | R-3 | R-3 | R-3 | 0 | 4 | [ r3*r1, r1*r2*r3*r1*r2*r3*r2 ] | 15.52.50.46. | |
| 95 | *3x | b | N | 8 | -1/3 | R-3c | R3c | R3m | 0 | 4 | [ r3, r1*r3*r1, r1*r2*r3*r1*r2*r3*r2 ] | 48.46.45.51. |
| 96 | *2626 | N | 8 | -1/3 | R-3m | R-3 | R-3m | 396 | 4 | [ r1, r3 ] | 48.36.47.50. | |
| 97 | 22*3 | b | N | 8 | -1/3 | R-3m | R32 | R32 | 0 | 4 | [ r1, r3*r1*r3, r2*r3*r2*r1*r3*r2 ] | 49.37.47.46. |
| 98 | *3x | a | N | 8 | -1/3 | R3m | R3c | R-3c | 0 | 4 | [ r1, r3*r1*r3, r2*r3*r1*r2*r3*r2*r3 ] | 40.52.47.51. |
| 99 | 22*3 | a | N | 8 | -1/3 | R32 | R32 | R-3m | 0 | 4 | [ r3, r1*r3*r1, r2*r3*r2*r1*r3*r2 ] | 49.48.42.52. |
| 100 | 2*222 | b | Y | 6 | -1/4 | Immm | Ibca | Pnnn | 0 | 1 | [ r2, r3*r2*r3, r1*r3*r2*r3*r1, r3*r1*r3*r1*r3*r1 ] | 67.71.72.54.55.53.69. |