Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
712 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11724596 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | D3×#3788 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11724246 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11723110 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#63785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11722711 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11722710 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10593842 | — | 3 | 1 | no | maximal |
| 9 | Q8×C3⋊(C3⋊D3) | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | C3×#3832 | C22 | 1 | 1 | yes | characteristic |
| 11 | C32×#239 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | #89026 | — | 2 | 1 | no | — |
| 13 | #89026 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | C4×D3×C3⋊D3 | — | 2 | 1 | no | — |
| 15 | C4×D3×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 16 | #89021 | — | 2 | 1 | no | — |
| 17 | #89021 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | #89014 | — | 2 | 1 | no | — |
| 19 | #89014 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4×C3⋊#157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #88989 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C3×C4×#157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×#3788 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #88926 | — | 2 | 1 | no | — |
| 25 | D3×#622 | — | 2 | 1 | no | — |
| 26 | Dic3⋊#157 | — | 2 | 1 | no | — |
| 27 | (C2×D3)⋊#157 | — | 2 | 1 | no | — |
| 28 | #41×C3⋊D3 | — | 3 | 1 | no | — |
| 29 | #64319 | — | 6 | 2 | no | — |
| 30 | #64286 | — | 3 | 1 | no | — |
| 31 | C2×#3788 | — | 3 | 1 | no | — |
| 32 | #63785 | — | 3 | 1 | no | — |
| 33 | #63785 | D3 | 1 | 1 | yes | characteristic, complemented |
| 34 | #63783 | — | 3 | 1 | no | — |
| 35 | #63783 | — | 3 | 1 | no | — |
| 36 | C2×D3×C3⋊D3 | — | 2 | 1 | no | — |
| 37 | C2×D3×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 38 | C2×C3⋊#157 | — | 2 | 1 | no | — |
| 39 | C2×C3×#157 | — | 2 | 1 | no | — |
| 40 | C33×Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | C4×C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 42 | C4×C3⋊(C3⋊D3) | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | #6308 | — | 2 | 1 | no | — |
| 44 | #6308 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C3×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 46 | C3×C4⋊(C3⋊D3) | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | C3×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 48 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 49 | C32×D12 | — | 2 | 1 | no | — |
| 50 | C32×D12 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C32×C4×D3 | — | 2 | 1 | no | — |
| 52 | C32×C4×D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | #6290 | — | 2 | 1 | no | — |
| 54 | #6290 | — | 2 | 1 | no | — |
| 55 | #6290 | — | 2 | 1 | no | — |
| 56 | #6289 | D4 | 1 | 1 | yes | characteristic |
| 57 | Dic3×C3⋊D3 | — | 2 | 1 | no | — |
| 58 | Dic3×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 59 | D3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 60 | D3×C3⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 61 | C3⋊#622 | — | 2 | 1 | no | — |
| 62 | C3×#622 | — | 2 | 1 | no | — |
| 63 | #4821 | — | 9 | 1 | no | maximal |
| 64 | C32×#41 | — | 3 | 1 | no | — |
| 65 | #3832 | C2×D3 | 1 | 1 | yes | characteristic |
| 66 | Q8×C3⋊D3 | — | 3 | 1 | no | — |
| 67 | Q8×C3⋊D3 | — | 6 | 2 | no | — |
| 68 | Q8×C3⋊D3 | — | 12 | 2 | no | — |
| 69 | #3830 | — | 3 | 1 | no | — |
| 70 | #3830 | — | 6 | 1 | no | — |
| 71 | D4×C3⋊D3 | — | 3 | 1 | no | — |
| 72 | D4×C3⋊D3 | — | 6 | 1 | no | — |
| 73 | #3828 | — | 3 | 1 | no | — |
| 74 | #3828 | — | 6 | 1 | no | — |
| 75 | C2×C4×C3⋊D3 | — | 3 | 1 | no | — |
| 76 | C2×C4×C3⋊D3 | — | 6 | 1 | no | — |
| 77 | C3×#239 | — | 2 | 2 | no | — |
| 78 | C3×#239 | — | 6 | 2 | no | — |
| 79 | #3802 | — | 6 | 2 | no | — |
| 80 | #3802 | — | 6 | 4 | no | — |
| 81 | C4×D32 | — | 6 | 2 | no | — |
| 82 | C4×D32 | — | 6 | 4 | no | — |
| 83 | #3795 | — | 6 | 2 | no | — |
| 84 | #3795 | — | 6 | 4 | no | — |
| 85 | #3795 | — | 6 | 2 | no | — |
| 86 | #3795 | — | 6 | 4 | no | — |
| 87 | C22⋊#157 | — | 6 | 1 | no | — |
| 88 | C2×#622 | — | 6 | 1 | no | — |
| 89 | C4⋊#157 | — | 6 | 1 | no | — |
| 90 | C4×#157 | — | 3 | 1 | no | — |
| 91 | C4×#157 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 92 | #3788 | — | 3 | 1 | no | — |
| 93 | #3788 | — | 6 | 1 | no | — |
| 94 | #3788 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 95 | C2×C3⋊(C3⋊D3) | C22⋊C4 | 1 | 1 | yes | characteristic |
| 96 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 97 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C2×C32×D3 | — | 2 | 1 | no | — |
| 99 | C2×C32×D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 100 | D3×C3⋊D3 | — | 4 | 1 | no | — |
| 101 | D3×C3⋊D3 | — | 4 | 2 | no | — |
| 102 | C3⋊#157 | — | 4 | 1 | no | — |
| 103 | C3×#157 | — | 4 | 1 | no | — |
| 104 | C33×C4 | — | 2 | 1 | no | — |
| 105 | C33×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 106 | C3⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 107 | C3⋊(C3⋊Dic3) | C22⋊C4 | 1 | 1 | yes | characteristic |
| 108 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C32×Dic3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 110 | D3×#41 | — | 9 | 1 | no | — |
| 111 | D3×#41 | — | 18 | 2 | no | — |
| 112 | D3×M16 | — | 9 | 1 | no | — |
| 113 | #872 | — | 9 | 1 | no | — |
| 114 | C3×#104 | — | 9 | 1 | no | — |
| 115 | #837 | — | 9 | 1 | no | — |
| 116 | #825 | — | 9 | 1 | no | — |
| 117 | #805 | — | 9 | 1 | no | — |
| 118 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 119 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 120 | C2×D32 | — | 6 | 2 | no | — |
| 121 | C2×D32 | — | 6 | 4 | no | — |
| 122 | C2×#157 | — | 2 | 1 | no | — |
| 123 | C2×#157 | — | 6 | 1 | no | — |
| 124 | C32×Q8 | — | 2 | 2 | no | — |
| 125 | C32×Q8 | — | 4 | 2 | no | — |
| 126 | C32×Q8 | C4×D3 | 1 | 1 | yes | characteristic |
| 127 | C32×D4 | — | 3 | 1 | no | — |
| 128 | C32×D4 | — | 6 | 1 | no | — |
| 129 | C2×C32×C4 | — | 3 | 1 | no | — |
| 130 | C2×C32×C4 | — | 6 | 1 | no | — |
| 131 | #638 | — | 6 | 1 | no | — |
| 132 | #638 | — | 6 | 1 | no | — |
| 133 | #638 | — | 6 | 1 | no | — |
| 134 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 135 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 136 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 137 | C4⋊(C3⋊D3) | C4×D3 | 1 | 1 | yes | characteristic |
| 138 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 139 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 140 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 141 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 142 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 143 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 144 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 145 | C4×C3⋊D3 | — | 6 | 4 | no | — |
| 146 | C4×C3⋊D3 | — | 12 | 4 | no | — |
| 147 | C4×C3⋊D3 | — | 12 | 2 | no | — |
| 148 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 149 | #634 | — | 3 | 1 | no | — |
| 150 | #634 | — | 6 | 2 | no | — |
| 151 | #634 | — | 6 | 1 | no | — |
| 152 | #634 | — | 6 | 4 | no | — |
| 153 | #634 | — | 12 | 4 | no | — |
| 154 | #634 | — | 12 | 2 | no | — |
| 155 | C3×D12 | — | 2 | 4 | no | — |
| 156 | C3×D12 | — | 2 | 2 | no | — |
| 157 | C3×D12 | — | 6 | 2 | no | — |
| 158 | C3×D12 | — | 6 | 4 | no | — |
| 159 | C3×C4×D3 | — | 2 | 4 | no | — |
| 160 | C3×C4×D3 | — | 2 | 2 | no | — |
| 161 | C3×C4×D3 | — | 6 | 2 | no | — |
| 162 | C3×C4×D3 | — | 6 | 4 | no | — |
| 163 | #625 | — | 6 | 4 | no | — |
| 164 | #625 | — | 6 | 4 | no | — |
| 165 | #625 | — | 6 | 4 | no | — |
| 166 | #624 | — | 6 | 2 | no | — |
| 167 | D3×Dic3 | — | 6 | 2 | no | — |
| 168 | D3×Dic3 | — | 6 | 2 | no | — |
| 169 | D3×Dic3 | — | 6 | 4 | no | — |
| 170 | D3×Dic3 | — | 6 | 4 | no | — |
| 171 | #622 | — | 2 | 1 | no | — |
| 172 | #622 | — | 6 | 1 | no | — |
| 173 | #421 | — | 27 | 1 | no | Sylow |
| 174 | C2×C33 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 175 | C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 176 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 177 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 178 | C32×D3 | — | 2 | 1 | no | — |
| 179 | C32×D3 | — | 4 | 1 | no | — |
| 180 | C3×#41 | — | 6 | 2 | no | — |
| 181 | C3×#41 | — | 9 | 1 | no | — |
| 182 | #239 | — | 6 | 2 | no | — |
| 183 | #239 | #157 | 1 | 1 | yes | characteristic, complemented |
| 184 | D3×Q8 | — | 9 | 1 | no | — |
| 185 | D3×Q8 | — | 18 | 2 | no | — |
| 186 | D3×Q8 | — | 36 | 2 | no | — |
| 187 | #237 | — | 9 | 1 | no | — |
| 188 | #237 | — | 18 | 2 | no | — |
| 189 | #237 | — | 18 | 1 | no | — |
| 190 | #237 | — | 18 | 4 | no | — |
| 191 | D3×D4 | — | 9 | 1 | no | — |
| 192 | D3×D4 | — | 18 | 2 | no | — |
| 193 | D3×D4 | — | 18 | 1 | no | — |
| 194 | D3×D4 | — | 18 | 4 | no | — |
| 195 | #235 | — | 9 | 1 | no | — |
| 196 | #235 | — | 18 | 2 | no | — |
| 197 | #235 | — | 18 | 1 | no | — |
| 198 | #235 | — | 18 | 4 | no | — |
| 199 | C2×C4×D3 | — | 9 | 1 | no | — |
| 200 | C2×C4×D3 | — | 18 | 2 | no | — |
| 201 | C2×C4×D3 | — | 18 | 1 | no | — |
| 202 | C2×C4×D3 | — | 18 | 4 | no | — |
| 203 | C3×M16 | — | 9 | 1 | no | — |
| 204 | C3×C42 | — | 9 | 1 | no | — |
| 205 | (C2×D3)⋊C4 | — | 18 | 1 | no | — |
| 206 | Dic3⋊C4 | — | 18 | 1 | no | — |
| 207 | C4×Dic3 | — | 9 | 1 | no | — |
| 208 | #208 | — | 9 | 1 | no | — |
| 209 | ΓL(1,𝔽25) | — | 18 | 1 | no | — |
| 210 | D3×C8 | — | 18 | 1 | no | — |
| 211 | C22×C32 | — | 3 | 1 | no | — |
| 212 | C22×C32 | — | 6 | 1 | no | — |
| 213 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 214 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 215 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 216 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 217 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 218 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 219 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 220 | C2×C3×D3 | — | 2 | 4 | no | — |
| 221 | C2×C3×D3 | — | 2 | 2 | no | — |
| 222 | C2×C3×D3 | — | 6 | 2 | no | — |
| 223 | C2×C3×D3 | — | 6 | 4 | no | — |
| 224 | D32 | — | 12 | 4 | no | — |
| 225 | D32 | — | 12 | 8 | no | — |
| 226 | #157 | — | 4 | 1 | no | — |
| 227 | #157 | — | 12 | 1 | no | — |
| 228 | C32×C4 | — | 2 | 1 | no | — |
| 229 | C32×C4 | — | 2 | 4 | no | — |
| 230 | C32×C4 | — | 2 | 2 | no | — |
| 231 | C32×C4 | — | 3 | 1 | no | — |
| 232 | C32×C4 | — | 4 | 4 | no | — |
| 233 | C32×C4 | — | 4 | 2 | no | — |
| 234 | C32×C4 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 235 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 236 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 237 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 238 | C3⋊Dic3 | — | 6 | 4 | no | — |
| 239 | C3⋊Dic3 | — | 12 | 4 | no | — |
| 240 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 241 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 242 | C3×Dic3 | — | 2 | 2 | no | — |
| 243 | C3×Dic3 | — | 6 | 2 | no | — |
| 244 | C2×#41 | — | 27 | 1 | no | — |
| 245 | C2×M16 | — | 27 | 1 | no | — |
| 246 | #117 | — | 27 | 1 | no | — |
| 247 | #104 | — | 9 | 1 | no | — |
| 248 | #104 | — | 27 | 1 | no | — |
| 249 | #104 | — | 27 | 1 | no | — |
| 250 | #104 | — | 27 | 1 | no | — |
| 251 | C33 | #421 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 252 | C22×D3 | — | 9 | 1 | no | — |
| 253 | C22×D3 | — | 18 | 2 | no | — |
| 254 | C22×D3 | — | 18 | 1 | no | — |
| 255 | C22×D3 | — | 18 | 4 | no | — |
| 256 | C3×Q8 | — | 2 | 2 | no | — |
| 257 | C3×Q8 | — | 4 | 2 | no | — |
| 258 | C3×Q8 | C2×#157 | 1 | 1 | yes | characteristic |
| 259 | C3×D4 | — | 6 | 2 | no | — |
| 260 | C3×D4 | — | 6 | 4 | no | — |
| 261 | C3×D4 | — | 9 | 1 | no | — |
| 262 | C3×D4 | — | 18 | 1 | no | — |
| 263 | C2×C3×C4 | — | 6 | 2 | no | — |
| 264 | C2×C3×C4 | — | 6 | 4 | no | — |
| 265 | C2×C3×C4 | — | 9 | 1 | no | — |
| 266 | C2×C3×C4 | — | 18 | 1 | no | — |
| 267 | C2×C3×C4 | — | 18 | 1 | no | — |
| 268 | #67 | — | 18 | 1 | no | — |
| 269 | #67 | — | 18 | 1 | no | — |
| 270 | #67 | — | 18 | 4 | no | — |
| 271 | #67 | — | 18 | 4 | no | — |
| 272 | #67 | — | 18 | 4 | no | — |
| 273 | #67 | — | 18 | 1 | no | — |
| 274 | C2×Dic3 | — | 9 | 1 | no | — |
| 275 | C2×Dic3 | — | 18 | 2 | no | — |
| 276 | C2×Dic3 | — | 18 | 4 | no | — |
| 277 | C2×Dic3 | — | 18 | 1 | no | — |
| 278 | C2×Dic3 | — | 18 | 1 | no | — |
| 279 | D12 | — | 2 | 1 | no | — |
| 280 | D12 | — | 6 | 2 | no | — |
| 281 | D12 | — | 6 | 4 | no | — |
| 282 | D12 | C2×#157 | 1 | 1 | yes | characteristic |
| 283 | C4×D3 | — | 2 | 1 | no | — |
| 284 | C4×D3 | — | 6 | 2 | no | — |
| 285 | C4×D3 | — | 6 | 4 | no | — |
| 286 | C4×D3 | — | 9 | 1 | no | — |
| 287 | C4×D3 | — | 9 | 1 | no | — |
| 288 | C4×D3 | — | 9 | 1 | no | — |
| 289 | C4×D3 | — | 18 | 2 | no | — |
| 290 | C4×D3 | — | 18 | 2 | no | — |
| 291 | C4×D3 | — | 18 | 2 | no | — |
| 292 | C4×D3 | — | 18 | 1 | no | — |
| 293 | C4×D3 | — | 18 | 4 | no | — |
| 294 | C4×D3 | — | 18 | 4 | no | — |
| 295 | C4×D3 | — | 18 | 1 | no | — |
| 296 | C4×D3 | — | 36 | 2 | no | — |
| 297 | C4×D3 | — | 36 | 4 | no | — |
| 298 | C4×D3 | C2×#157 | 1 | 1 | yes | characteristic |
| 299 | Dic6 | — | 9 | 1 | no | — |
| 300 | Dic6 | — | 18 | 2 | no | — |
| 301 | Dic6 | — | 18 | 1 | no | — |
| 302 | Dic6 | — | 18 | 4 | no | — |
| 303 | Dic6 | — | 36 | 2 | no | — |
| 304 | Dic6 | — | 36 | 4 | no | — |
| 305 | C3×C8 | — | 18 | 1 | no | — |
| 306 | C3⋊C8 | — | 18 | 1 | no | — |
| 307 | C2×C32 | — | 2 | 2 | no | — |
| 308 | C2×C32 | — | 4 | 2 | no | — |
| 309 | C2×C32 | — | 6 | 1 | no | — |
| 310 | C2×C32 | — | 12 | 1 | no | — |
| 311 | C2×C32 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 312 | C3⋊D3 | — | 2 | 1 | no | — |
| 313 | C3⋊D3 | — | 4 | 1 | no | — |
| 314 | C3⋊D3 | — | 6 | 1 | no | — |
| 315 | C3⋊D3 | — | 6 | 4 | no | — |
| 316 | C3⋊D3 | — | 12 | 4 | no | — |
| 317 | C3×D3 | — | 4 | 2 | no | — |
| 318 | C3×D3 | — | 4 | 4 | no | — |
| 319 | C3×D3 | — | 12 | 2 | no | — |
| 320 | C3×D3 | — | 12 | 4 | no | — |
| 321 | #41 | — | 3 | 1 | no | — |
| 322 | #41 | — | 9 | 1 | no | — |
| 323 | #41 | — | 27 | 1 | no | — |
| 324 | #41 | — | 27 | 1 | no | — |
| 325 | #41 | — | 54 | 1 | no | — |
| 326 | #41 | — | 54 | 1 | no | — |
| 327 | C2×Q8 | — | 27 | 1 | no | — |
| 328 | C2×D4 | — | 27 | 1 | no | — |
| 329 | C2×D4 | — | 54 | 1 | no | — |
| 330 | C22×C4 | — | 27 | 1 | no | — |
| 331 | C22×C4 | — | 54 | 1 | no | — |
| 332 | M16 | — | 9 | 1 | no | — |
| 333 | M16 | — | 27 | 1 | no | — |
| 334 | M16 | — | 54 | 1 | no | — |
| 335 | C2×C8 | — | 54 | 1 | no | — |
| 336 | C4⋊C4 | — | 54 | 1 | no | — |
| 337 | C22⋊C4 | — | 54 | 1 | no | — |
| 338 | C42 | — | 9 | 1 | no | — |
| 339 | C42 | — | 27 | 1 | no | — |
| 340 | C22×C3 | — | 6 | 2 | no | — |
| 341 | C22×C3 | — | 6 | 4 | no | — |
| 342 | C22×C3 | — | 9 | 1 | no | — |
| 343 | C22×C3 | — | 18 | 1 | no | — |
| 344 | C2×D3 | — | 2 | 1 | no | — |
| 345 | C2×D3 | — | 6 | 2 | no | — |
| 346 | C2×D3 | — | 6 | 4 | no | — |
| 347 | C2×D3 | — | 9 | 1 | no | — |
| 348 | C2×D3 | — | 18 | 2 | no | — |
| 349 | C2×D3 | — | 36 | 2 | no | — |
| 350 | C2×D3 | — | 36 | 1 | no | — |
| 351 | C2×D3 | — | 36 | 2 | no | — |
| 352 | C2×D3 | — | 36 | 4 | no | — |
| 353 | C2×D3 | — | 36 | 8 | no | — |
| 354 | C2×D3 | C22⋊#157 | 1 | 1 | yes | characteristic |
| 355 | C3×C4 | — | 2 | 4 | no | — |
| 356 | C3×C4 | — | 2 | 1 | no | — |
| 357 | C3×C4 | — | 2 | 2 | no | — |
| 358 | C3×C4 | — | 4 | 4 | no | — |
| 359 | C3×C4 | — | 4 | 2 | no | — |
| 360 | C3×C4 | — | 6 | 2 | no | — |
| 361 | C3×C4 | — | 9 | 1 | no | — |
| 362 | C3×C4 | — | 36 | 1 | no | — |
| 363 | C3×C4 | C22×#157 | 1 | 1 | yes | characteristic |
| 364 | Dic3 | — | 6 | 2 | no | — |
| 365 | Dic3 | — | 9 | 1 | no | — |
| 366 | Dic3 | — | 18 | 2 | no | — |
| 367 | Dic3 | — | 18 | 4 | no | — |
| 368 | Dic3 | — | 18 | 1 | no | — |
| 369 | Dic3 | — | 36 | 2 | no | — |
| 370 | Dic3 | — | 36 | 4 | no | — |
| 371 | Dic3 | — | 36 | 1 | no | — |
| 372 | Dic3 | C22⋊#157 | 1 | 1 | yes | characteristic |
| 373 | C32 | — | 2 | 2 | no | — |
| 374 | C32 | — | 4 | 2 | no | — |
| 375 | C32 | #4821 | 1 | 1 | yes | characteristic, complemented |
| 376 | C23 | — | 27 | 1 | no | — |
| 377 | C23 | — | 54 | 1 | no | — |
| 378 | Q8 | — | 27 | 1 | no | — |
| 379 | Q8 | — | 54 | 1 | no | — |
| 380 | Q8 | D3×#157 | 1 | 1 | yes | characteristic |
| 381 | D4 | — | 3 | 1 | no | — |
| 382 | D4 | — | 6 | 1 | no | — |
| 383 | D4 | — | 9 | 1 | no | — |
| 384 | D4 | — | 18 | 1 | no | — |
| 385 | D4 | — | 54 | 1 | no | — |
| 386 | D4 | — | 54 | 1 | no | — |
| 387 | D4 | — | 54 | 1 | no | — |
| 388 | C2×C4 | — | 3 | 1 | no | — |
| 389 | C2×C4 | — | 6 | 1 | no | — |
| 390 | C2×C4 | — | 9 | 1 | no | — |
| 391 | C2×C4 | — | 18 | 1 | no | — |
| 392 | C2×C4 | — | 18 | 1 | no | — |
| 393 | C2×C4 | — | 27 | 1 | no | — |
| 394 | C2×C4 | — | 27 | 1 | no | — |
| 395 | C2×C4 | — | 27 | 1 | no | — |
| 396 | C2×C4 | — | 27 | 1 | no | — |
| 397 | C2×C4 | — | 54 | 1 | no | — |
| 398 | C2×C4 | — | 54 | 1 | no | — |
| 399 | C2×C4 | — | 54 | 1 | no | — |
| 400 | C2×C4 | — | 54 | 1 | no | — |
| 401 | C8 | — | 18 | 1 | no | — |
| 402 | C8 | — | 54 | 1 | no | — |
| 403 | C2×C3 | — | 2 | 2 | no | — |
| 404 | C2×C3 | — | 4 | 2 | no | — |
| 405 | C2×C3 | — | 12 | 2 | no | — |
| 406 | C2×C3 | — | 12 | 4 | no | — |
| 407 | C2×C3 | — | 18 | 1 | no | — |
| 408 | C2×C3 | — | 36 | 1 | no | — |
| 409 | C2×C3 | C2×C22⋊#157 | 1 | 1 | yes | characteristic |
| 410 | D3 | — | 2 | 1 | no | — |
| 411 | D3 | — | 4 | 1 | no | — |
| 412 | D3 | — | 12 | 2 | no | — |
| 413 | D3 | — | 12 | 4 | no | — |
| 414 | D3 | — | 18 | 4 | no | — |
| 415 | D3 | — | 18 | 1 | no | — |
| 416 | D3 | — | 36 | 4 | no | — |
| 417 | C22 | — | 3 | 1 | no | — |
| 418 | C22 | — | 6 | 1 | no | — |
| 419 | C22 | — | 9 | 1 | no | — |
| 420 | C22 | — | 18 | 1 | no | — |
| 421 | C22 | — | 27 | 1 | no | — |
| 422 | C22 | — | 108 | 1 | no | — |
| 423 | C22 | — | 108 | 2 | no | — |
| 424 | C4 | — | 2 | 1 | no | — |
| 425 | C4 | — | 3 | 1 | no | — |
| 426 | C4 | — | 9 | 1 | no | — |
| 427 | C4 | — | 27 | 1 | no | — |
| 428 | C4 | — | 36 | 1 | no | — |
| 429 | C4 | — | 54 | 1 | no | — |
| 430 | C4 | — | 108 | 1 | no | — |
| 431 | C4 | C2×D3×#157 | 1 | 1 | yes | characteristic |
| 432 | C3 | — | 2 | 2 | no | — |
| 433 | C3 | — | 4 | 2 | no | — |
| 434 | C3 | #10593842 | 1 | 1 | yes | characteristic, complemented |
| 435 | C2 | — | 6 | 1 | no | — |
| 436 | C2 | — | 12 | 1 | no | — |
| 437 | C2 | — | 18 | 1 | no | — |
| 438 | C2 | — | 36 | 1 | no | — |
| 439 | C2 | — | 54 | 1 | no | — |
| 440 | C2 | D3×C22⋊#157 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. D3×#3788 | C2 | semidirect |
| 3. #11724246 | C2 | semidirect |
| 4. #11723110 | C2 | semidirect |
| 5. C3×#63785 | C2 | semidirect |
| 6. #11722711 | C2 | semidirect |
| 7. #11722710 | C2 | semidirect |
| 9. Q8×C3⋊(C3⋊D3) | C4 | semidirect |
| 11. C32×#239 | C4 | semidirect |
| 13. #89026 | C4 | semidirect |
| 17. #89021 | C4 | semidirect |
| 20. C4×C3⋊#157 | C22 | semidirect |
| 21. #88989 | C22 | semidirect |
| 22. C3×C4×#157 | C22 | semidirect |
| 23. C3×#3788 | C22 | semidirect |
| 33. #63785 | D3 | semidirect |
| 91. C4×#157 | C2×D3 | semidirect |
| 94. #3788 | C2×D3 | semidirect |
| 183. #239 | #157 | semidirect |
| 251. C33 | #421 | semidirect |
| 375. C32 | #4821 | semidirect |
| 434. C3 | #10593842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724596 | 2 |
| D3×#3788 | 2 |
| #11724246 | 2 |
| #11723110 | 2 |
| C3×#63785 | 2 |
| #11722711 | 2 |
| #11722710 | 2 |
| #10593842 | 3 |
| #4821 | 9 |