| Number | Orbifold | Embedding | Normal | Subgroup index | Curvature | P spacegroup | G spacegroup | D spacegroup | Utiling count | Conjugacy class size | Generators | Maximal subgroups |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 101 | *22222 | b | N | 6 | -1/4 | Fmmm | Fddd | Cmma | 893 | 3 | [ r1, r2, r3*r1*r3*r1*r3, r3*r1*r2*r3*r2*r1*r3 ] | 75.76.70.71.83.59.57.90.91.89.88. |
| 102 | *22222 | a | N | 6 | -1/4 | P4/mmm | I4122 | P4222 | 889 | 3 | [ r1, r2, r3*r2*r3 ] | 66.65.77.60.57.73.55. |
| 103 | *2244 | b | N | 6 | -1/4 | P4/nmm | I41/a | I41/amd | 370 | 3 | [ r1, r3*r2*r3, r3*r1*r3*r1*r3 ] | 67.87.64.80.83.60.62. |
| 104 | 2*222 | a | N | 6 | -1/4 | P42/nnm | Ibca | I41/amd | 0 | 3 | [ r1, r3*r2*r3*r2, r3*r1*r3*r1*r3 ] | 65.63.83.58.82.54.81. |
| 105 | **2 | b | N | 6 | -1/4 | I4mm | I41cd | I41/acd | 0 | 3 | [ r1, r3*r2*r3, r3*r1*r3*r1*r3*r2 ] | 63.61.59.56.60.69.68. |
| 106 | 4*22 | N | 6 | -1/4 | P42/mnm | I-4c2 | P-4n2 | 0 | 3 | [ r1, r2, r3*r1*r3*r2*r1*r3 ] | 74.63.62.72.57.78.79. | |
| 107 | *2244 | a | N | 6 | -1/4 | P42/mmc | I-42d | P-42m | 366 | 3 | [ r2, r3, r1*r3*r2*r3*r1 ] | 74.86.70.55.68.64.81. |
| 108 | 2*44 | N | 6 | -1/4 | I-4m2 | I-4c2 | I41/amd | 0 | 3 | [ r2, r3, r1*r3*r2*r1*r3*r1 ] | 84.64.66.82.78.69.75. | |
| 109 | 24* | b | N | 6 | -1/4 | I4/m | I41/a | P42/n | 0 | 3 | [ r2, r3*r2*r3*r1, r3*r1*r3*r1*r3*r1 ] | 74.84.87.71.58.73.56. |
| 110 | 24* | a | N | 6 | -1/4 | I-42m | I-42d | I41/acd | 0 | 3 | [ r1, r3*r2*r3*r2, r3*r1*r3*r1*r3*r2 ] | 85.84.65.86.62.59.53. |
| 111 | 22*2 | b | N | 6 | -1/4 | P42/nmc | Fddd | I41/acd | 0 | 3 | [ r2, r3*r2*r3, r1*r3*r2*r1*r3*r1, r3*r1*r3*r1*r3*r1 ] | 85.67.76.58.66.79.68. |
| 112 | **2 | a | N | 6 | -1/4 | P4/mnc | I41cd | P42nm | 0 | 3 | [ r2, r3*r2*r3*r1, r3*r1*r3*r1*r3 ] | 85.70.80.72.73.82.61. |
| 113 | 22*2 | a | N | 6 | -1/4 | I422 | I4122 | I41/amd | 0 | 3 | [ r2*r1, r3*r2*r3*r1, r3*r1*r3*r1*r3 ] | 75.77.81.80.56.79.53. |
| 114 | 2224 | N | 6 | -1/4 | P4/nnc | I41/acd | I41/acd | 0 | 3 | [ r2*r1, r3*r2*r3*r1, r3*r1*r3*r1*r3*r1 ] | 87.77.61.54.78.76.86. | |
| 115 | 3*22 | Y | 4 | -1/6 | Pm-3 | I213 | P23 | 0 | 1 | [ r2, r3*r1*r3*r1 ] | 92.55.46. | |
| 116 | 344 | Y | 4 | -1/6 | P-43n | I-43d | F-43c | 0 | 1 | [ r3*r2, r1*r3*r2*r1 ] | 92.86.51. | |
| 117 | 2*33 | Y | 4 | -1/6 | P-43m | I213 | F4132 | 0 | 1 | [ r1, r3*r1*r3, r3*r2*r3*r2 ] | 92.65.47. | |
| 118 | 2223 | Y | 4 | -1/6 | P432 | I4132 | F4132 | 0 | 1 | [ r2*r1, r3*r1*r3*r1 ] | 92.49.77. | |
| 119 | *2323 | Y | 4 | -1/6 | P4232 | I213 | F-43m | 183 | 1 | [ r3, r1*r3*r1, r2*r3*r2 ] | 92.48.81. | |
| 120 | 266 | Y | 4 | -1/6 | Pn-3 | Ia-3 | Fd-3 | 0 | 1 | [ r3*r1, r2*r3*r2*r1 ] | 92.54.50. | |
| 121 | 23x | Y | 4 | -1/6 | I23 | I213 | Fd-3 | 0 | 1 | [ r1*r2*r3, r1*r3*r2 ] | 92.52.53. | |
| 122 | 2*26 | N | 4 | -1/6 | R-3m | R-3c | R-3m | 0 | 4 | [ r1, r3, r2*r3*r2*r1*r3*r2 ] | 98.99.93.96.97.94.95.89. | |
| 123 | *2224 | N | 3 | -1/8 | I4/mmm | I41/acd | P42/nnm | 694 | 3 | [ r1, r2, r3*r2*r3, r3*r1*r3*r1*r3 ] | 107.101.100.114.106.105.104.110.111.112.113.103.102.109.108. | |
| 124 | *2223 | Y | 2 | -1/12 | Pm-3m | I4132 | P4232 | 336 | 1 | [ r1, r2, r3*r1*r3 ] | 115.117.118.102.97. | |
| 125 | *344 | Y | 2 | -1/12 | Pm-3n | I-43d | P-43m | 108 | 1 | [ r2, r3, r1*r3*r1 ] | 107.115.116.119.95. | |
| 126 | 6*2 | Y | 2 | -1/12 | Im-3 | Ia-3 | Pn-3 | 0 | 1 | [ r2, r3*r1 ] | 115.121.120.94.100. | |
| 127 | *266 | Y | 2 | -1/12 | Pn-3m | Ia-3 | Fd-3m | 92 | 1 | [ r1, r3, r2*r3*r2 ] | 117.96.120.104.119. | |
| 128 | 4*3 | Y | 2 | -1/12 | I-43m | I-43d | Fd-3c | 0 | 1 | [ r1, r3*r2 ] | 110.116.117.121.98. | |
| 129 | 2*23 | Y | 2 | -1/12 | I432 | I4132 | Fd-3m | 0 | 1 | [ r2*r1, r3, r1*r3*r1 ] | 118.99.121.119.113. | |
| 130 | 246 | Y | 2 | -1/12 | Pn-3n | Ia-3d | Fd-3c | 0 | 1 | [ r2*r1, r3*r1 ] | 114.93.116.118.120. | |
| 131 | *246 | Y | 1 | -1/24 | Im-3m | Ia-3d | Pn-3m | 204 | 1 | [ r1, r2, r3 ] | 130.129.128.125.124.127.126.123.122. |