Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
814 conjugacy classes of subgroups.
The subgroup lattice has 362 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #81891 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #81760 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #81592 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #81556 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#1708 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71332 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #71254 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #71212 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #71180 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #68059 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | D3×C82 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #19596 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×#916 | — | 2 | 2 | no | — |
| 14 | #5728 | C22 | 1 | 2 | yes | — |
| 15 | #5725 | C22 | 1 | 1 | yes | characteristic |
| 16 | #5716 | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×#498 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#492 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×#487 | C22 | 1 | 2 | yes | — |
| 20 | C3×#486 | C22 | 1 | 2 | yes | — |
| 21 | #5168 | — | 2 | 2 | no | — |
| 22 | #5092 | C22 | 1 | 1 | yes | characteristic |
| 23 | #5085 | C22 | 1 | 2 | yes | — |
| 24 | #5080 | C22 | 1 | 2 | yes | — |
| 25 | #5080 | C22 | 1 | 2 | yes | — |
| 26 | #5078 | C22 | 1 | 2 | yes | — |
| 27 | #5076 | C22 | 1 | 2 | yes | — |
| 28 | #5073 | C22 | 1 | 1 | yes | characteristic |
| 29 | #4860 | — | 2 | 2 | no | — |
| 30 | #4858 | — | 2 | 2 | no | — |
| 31 | #4807 | — | 2 | 4 | no | — |
| 32 | #4788 | — | 2 | 4 | no | — |
| 33 | #4778 | — | 2 | 4 | no | — |
| 34 | #4758 | — | 2 | 4 | no | — |
| 35 | #4694 | C22 | 1 | 2 | yes | — |
| 36 | #4693 | C22 | 1 | 1 | yes | characteristic |
| 37 | C4×D3×C8 | C22 | 1 | 1 | yes | characteristic |
| 38 | C4×D3×C8 | C22 | 1 | 2 | yes | — |
| 39 | #4681 | C22 | 1 | 2 | yes | — |
| 40 | #4680 | C22 | 1 | 1 | yes | characteristic |
| 41 | C3×C82 | C22 | 1 | 1 | yes | characteristic |
| 42 | C8×C3⋊C8 | C22 | 1 | 2 | yes | — |
| 43 | C8×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 44 | #3167 | — | 3 | 2 | no | — |
| 45 | #3167 | — | 3 | 2 | no | — |
| 46 | #3160 | — | 3 | 1 | no | — |
| 47 | #3147 | — | 3 | 1 | no | — |
| 48 | #1708 | — | 3 | 1 | no | — |
| 49 | #1708 | D3 | 1 | 1 | yes | characteristic, complemented |
| 50 | #1707 | — | 3 | 2 | no | — |
| 51 | #1706 | — | 3 | 2 | no | — |
| 52 | #1705 | — | 3 | 1 | no | — |
| 53 | #1705 | — | 3 | 1 | no | — |
| 54 | C2×C82 | — | 3 | 1 | no | — |
| 55 | C2×#239 | — | 2 | 1 | no | — |
| 56 | C2×#237 | — | 2 | 1 | no | — |
| 57 | C2×C3×SD16 | — | 2 | 2 | no | — |
| 58 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 59 | C3×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 60 | C3×#127 | C23 | 1 | 1 | yes | characteristic |
| 61 | #947 | — | 2 | 1 | no | — |
| 62 | #946 | — | 2 | 2 | no | — |
| 63 | Q8×Dic3 | — | 2 | 2 | no | — |
| 64 | C2×#216 | — | 2 | 2 | no | — |
| 65 | C2×#215 | — | 2 | 4 | no | — |
| 66 | #938 | — | 2 | 2 | no | — |
| 67 | #936 | — | 2 | 1 | no | — |
| 68 | D4×Dic3 | — | 2 | 2 | no | — |
| 69 | C2×#214 | — | 2 | 4 | no | — |
| 70 | C2×#213 | — | 2 | 2 | no | — |
| 71 | #916 | — | 4 | 8 | no | — |
| 72 | C2×#204 | — | 2 | 2 | no | — |
| 73 | C2×D3×C8 | D4 | 1 | 4 | yes | — |
| 74 | C2×D3×C8 | D4 | 1 | 2 | yes | — |
| 75 | #897 | — | 2 | 2 | no | — |
| 76 | #895 | — | 2 | 2 | no | — |
| 77 | #893 | — | 2 | 2 | no | — |
| 78 | #892 | — | 2 | 2 | no | — |
| 79 | #890 | — | 2 | 2 | no | — |
| 80 | #887 | — | 2 | 2 | no | — |
| 81 | #874 | C23 | 1 | 1 | yes | characteristic |
| 82 | C42×D3 | C23 | 1 | 1 | yes | characteristic |
| 83 | #869 | C23 | 1 | 2 | yes | — |
| 84 | #869 | C23 | 1 | 1 | yes | characteristic |
| 85 | C3×#106 | — | 2 | 2 | no | — |
| 86 | C3×#103 | — | 2 | 4 | no | — |
| 87 | C3×#102 | — | 2 | 4 | no | — |
| 88 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 89 | C3×C4×C8 | C23 | 1 | 2 | yes | — |
| 90 | #821 | — | 2 | 4 | no | — |
| 91 | #817 | — | 2 | 2 | no | — |
| 92 | #816 | — | 2 | 4 | no | — |
| 93 | C8×Dic3 | D4 | 1 | 2 | yes | — |
| 94 | C8×Dic3 | D4 | 1 | 4 | yes | — |
| 95 | #808 | — | 2 | 4 | no | — |
| 96 | #808 | — | 2 | 4 | no | — |
| 97 | #807 | — | 2 | 4 | no | — |
| 98 | C4×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 99 | C4×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 100 | C2×#135 | — | 6 | 2 | no | — |
| 101 | #533 | — | 3 | 2 | no | — |
| 102 | #532 | — | 3 | 1 | no | — |
| 103 | #532 | — | 3 | 1 | no | — |
| 104 | #500 | — | 3 | 2 | no | — |
| 105 | #499 | — | 6 | 2 | no | — |
| 106 | #498 | — | 3 | 2 | no | — |
| 107 | #498 | — | 3 | 2 | no | — |
| 108 | #498 | — | 3 | 1 | no | — |
| 109 | #498 | C2×D3 | 1 | 1 | yes | characteristic |
| 110 | #495 | — | 6 | 2 | no | — |
| 111 | #494 | — | 3 | 1 | no | — |
| 112 | #493 | — | 3 | 1 | no | — |
| 113 | #492 | — | 3 | 2 | no | — |
| 114 | #492 | — | 3 | 2 | no | — |
| 115 | #492 | — | 3 | 1 | no | — |
| 116 | #492 | C2×D3 | 1 | 1 | yes | characteristic |
| 117 | #487 | — | 3 | 2 | no | — |
| 118 | #487 | C2×D3 | 1 | 2 | yes | — |
| 119 | #486 | — | 3 | 2 | no | — |
| 120 | #486 | C2×D3 | 1 | 2 | yes | — |
| 121 | #465 | — | 6 | 4 | no | — |
| 122 | #465 | — | 6 | 4 | no | — |
| 123 | C4×SD16 | — | 6 | 4 | no | — |
| 124 | C4×SD16 | — | 6 | 4 | no | — |
| 125 | #427 | — | 6 | 2 | no | — |
| 126 | C2×C4×C8 | — | 3 | 1 | no | — |
| 127 | C2×C4×C8 | — | 3 | 2 | no | — |
| 128 | C82 | — | 3 | 1 | no | — |
| 129 | C82 | — | 3 | 2 | no | — |
| 130 | C82 | C2×D3 | 1 | 1 | yes | characteristic |
| 131 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 132 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 133 | C2×C3×D4 | — | 2 | 2 | no | — |
| 134 | C2×C3×D4 | — | 2 | 1 | no | — |
| 135 | C2×#67 | — | 4 | 1 | no | — |
| 136 | C22×Dic3 | — | 4 | 1 | no | — |
| 137 | #239 | — | 4 | 4 | no | — |
| 138 | #237 | — | 4 | 4 | no | — |
| 139 | C2×D12 | — | 2 | 2 | no | — |
| 140 | C2×D12 | — | 2 | 1 | no | — |
| 141 | C2×D12 | — | 4 | 1 | no | — |
| 142 | C2×C4×D3 | — | 4 | 1 | no | — |
| 143 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 144 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C2×Dic6 | — | 2 | 2 | no | — |
| 146 | C2×Dic6 | — | 2 | 1 | no | — |
| 147 | C3×SD16 | — | 4 | 4 | no | — |
| 148 | C2×C3×C8 | C2×D4 | 1 | 4 | yes | — |
| 149 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 150 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 151 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 152 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 153 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 154 | #217 | — | 4 | 2 | no | — |
| 155 | #216 | — | 4 | 4 | no | — |
| 156 | #215 | — | 4 | 8 | no | — |
| 157 | #214 | — | 4 | 8 | no | — |
| 158 | #213 | — | 4 | 4 | no | — |
| 159 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 160 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 161 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 162 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 163 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 164 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 165 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 166 | C4×Dic3 | — | 4 | 2 | no | — |
| 167 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 168 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 170 | C2×C3⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 171 | #204 | — | 4 | 4 | no | — |
| 172 | D3×C8 | — | 2 | 8 | no | — |
| 173 | D3×C8 | SD16 | 1 | 8 | yes | complemented |
| 174 | C2×#41 | — | 6 | 1 | no | — |
| 175 | C2×#41 | — | 6 | 1 | no | — |
| 176 | #135 | — | 12 | 8 | no | — |
| 177 | C2×Q16 | — | 6 | 2 | no | — |
| 178 | C2×SD16 | — | 2 | 2 | no | — |
| 179 | C2×SD16 | — | 6 | 4 | no | — |
| 180 | C2×SD16 | — | 6 | 4 | no | — |
| 181 | C2×SD16 | — | 6 | 2 | no | — |
| 182 | C2×D8 | — | 6 | 2 | no | — |
| 183 | C22×C8 | — | 3 | 2 | no | — |
| 184 | C22×C8 | — | 3 | 4 | no | — |
| 185 | C4⋊Q8 | — | 3 | 1 | no | — |
| 186 | C4⋊Q8 | — | 3 | 2 | no | — |
| 187 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 188 | C4⋊Q8 | C22×D3 | 1 | 2 | yes | — |
| 189 | #127 | — | 3 | 1 | no | — |
| 190 | #127 | C22×D3 | 1 | 1 | yes | characteristic |
| 191 | #125 | — | 6 | 2 | no | — |
| 192 | #124 | — | 6 | 1 | no | — |
| 193 | #124 | — | 6 | 1 | no | — |
| 194 | C22⋊Q8 | — | 6 | 2 | no | — |
| 195 | C22⋊Q8 | — | 6 | 2 | no | — |
| 196 | #121 | — | 6 | 2 | no | — |
| 197 | #121 | — | 6 | 2 | no | — |
| 198 | C4×Q8 | — | 6 | 2 | no | — |
| 199 | C4×Q8 | — | 6 | 2 | no | — |
| 200 | C4×D4 | — | 6 | 2 | no | — |
| 201 | C4×D4 | — | 6 | 2 | no | — |
| 202 | #117 | — | 6 | 2 | no | — |
| 203 | C2×C42 | — | 3 | 1 | no | — |
| 204 | #107 | — | 6 | 4 | no | — |
| 205 | #106 | — | 2 | 2 | no | — |
| 206 | #106 | — | 6 | 4 | no | — |
| 207 | #106 | — | 6 | 4 | no | — |
| 208 | #106 | — | 6 | 2 | no | — |
| 209 | #103 | — | 2 | 4 | no | — |
| 210 | #103 | — | 6 | 4 | no | — |
| 211 | #102 | — | 2 | 4 | no | — |
| 212 | #102 | — | 6 | 4 | no | — |
| 213 | C4×C8 | — | 3 | 4 | no | — |
| 214 | C4×C8 | — | 3 | 2 | no | — |
| 215 | C4×C8 | — | 3 | 2 | no | — |
| 216 | C4×C8 | — | 3 | 1 | no | — |
| 217 | C4×C8 | C22×D3 | 1 | 2 | yes | — |
| 218 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 219 | C23×C3 | — | 4 | 1 | no | — |
| 220 | C22×D3 | — | 4 | 1 | no | — |
| 221 | C22×D3 | #127 | 1 | 1 | yes | characteristic |
| 222 | C3×Q8 | — | 4 | 2 | no | — |
| 223 | C3×Q8 | — | 4 | 4 | no | — |
| 224 | C3×D4 | — | 4 | 2 | no | — |
| 225 | C3×D4 | — | 4 | 4 | no | — |
| 226 | C2×C3×C4 | — | 4 | 2 | no | — |
| 227 | C2×C3×C4 | — | 4 | 1 | no | — |
| 228 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 229 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 230 | #67 | — | 8 | 2 | no | — |
| 231 | C2×Dic3 | — | 4 | 2 | no | — |
| 232 | C2×Dic3 | — | 4 | 1 | no | — |
| 233 | C2×Dic3 | — | 8 | 2 | no | — |
| 234 | C2×Dic3 | #127 | 1 | 2 | yes | — |
| 235 | C2×Dic3 | #127 | 1 | 1 | yes | characteristic |
| 236 | D12 | — | 4 | 2 | no | — |
| 237 | D12 | — | 4 | 4 | no | — |
| 238 | D12 | — | 8 | 2 | no | — |
| 239 | C4×D3 | — | 2 | 4 | no | — |
| 240 | C4×D3 | — | 8 | 2 | no | — |
| 241 | C4×D3 | C2×SD16 | 1 | 4 | yes | — |
| 242 | Dic6 | — | 4 | 2 | no | — |
| 243 | Dic6 | — | 4 | 4 | no | — |
| 244 | C3×C8 | — | 2 | 4 | no | — |
| 245 | C3×C8 | C2×SD16 | 1 | 4 | yes | — |
| 246 | C3⋊C8 | C2×SD16 | 1 | 4 | yes | — |
| 247 | C3⋊C8 | #135 | 1 | 8 | yes | complemented |
| 248 | #41 | — | 12 | 4 | no | — |
| 249 | #41 | — | 12 | 4 | no | — |
| 250 | C2×Q8 | — | 2 | 2 | no | — |
| 251 | C2×Q8 | — | 2 | 1 | no | — |
| 252 | C2×Q8 | — | 6 | 2 | no | — |
| 253 | C2×Q8 | — | 6 | 1 | no | — |
| 254 | C2×D4 | — | 2 | 2 | no | — |
| 255 | C2×D4 | — | 2 | 1 | no | — |
| 256 | C2×D4 | — | 6 | 2 | no | — |
| 257 | C2×D4 | — | 6 | 1 | no | — |
| 258 | C2×D4 | — | 12 | 1 | no | — |
| 259 | C2×D4 | — | 12 | 1 | no | — |
| 260 | C22×C4 | — | 3 | 1 | no | — |
| 261 | C22×C4 | — | 3 | 2 | no | — |
| 262 | C22×C4 | — | 12 | 1 | no | — |
| 263 | C22×C4 | — | 12 | 1 | no | — |
| 264 | Q16 | — | 12 | 4 | no | — |
| 265 | SD16 | — | 4 | 4 | no | — |
| 266 | SD16 | — | 12 | 8 | no | — |
| 267 | SD16 | — | 12 | 8 | no | — |
| 268 | SD16 | — | 12 | 4 | no | — |
| 269 | D8 | — | 12 | 4 | no | — |
| 270 | C2×C8 | — | 3 | 4 | no | — |
| 271 | C2×C8 | — | 3 | 2 | no | — |
| 272 | C2×C8 | — | 3 | 8 | no | — |
| 273 | C2×C8 | — | 6 | 8 | no | — |
| 274 | C2×C8 | D3×D4 | 1 | 4 | yes | — |
| 275 | C2×C8 | D3×D4 | 1 | 2 | yes | — |
| 276 | C4⋊C4 | — | 2 | 2 | no | — |
| 277 | C4⋊C4 | — | 2 | 2 | no | — |
| 278 | C4⋊C4 | — | 2 | 2 | no | — |
| 279 | C4⋊C4 | — | 6 | 2 | no | — |
| 280 | C4⋊C4 | — | 6 | 2 | no | — |
| 281 | C4⋊C4 | — | 6 | 2 | no | — |
| 282 | C4⋊C4 | — | 12 | 2 | no | — |
| 283 | C4⋊C4 | — | 12 | 2 | no | — |
| 284 | C22⋊C4 | — | 12 | 2 | no | — |
| 285 | C22⋊C4 | — | 12 | 2 | no | — |
| 286 | C22⋊C4 | — | 12 | 2 | no | — |
| 287 | C42 | — | 3 | 2 | no | — |
| 288 | C42 | — | 3 | 1 | no | — |
| 289 | C42 | — | 12 | 2 | no | — |
| 290 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 291 | C22×C3 | — | 8 | 1 | no | — |
| 292 | C22×C3 | — | 8 | 2 | no | — |
| 293 | C22×C3 | C2×#127 | 1 | 1 | yes | characteristic |
| 294 | C2×D3 | — | 2 | 2 | no | — |
| 295 | C2×D3 | — | 8 | 1 | no | — |
| 296 | C2×D3 | — | 8 | 2 | no | — |
| 297 | C2×D3 | #492 | 1 | 2 | yes | — |
| 298 | C3×C4 | — | 8 | 1 | no | — |
| 299 | C3×C4 | — | 8 | 2 | no | — |
| 300 | C3×C4 | C22×SD16 | 1 | 2 | yes | — |
| 301 | C3×C4 | C2×#135 | 1 | 4 | yes | — |
| 302 | Dic3 | — | 2 | 2 | no | — |
| 303 | Dic3 | — | 8 | 1 | no | — |
| 304 | Dic3 | — | 8 | 2 | no | — |
| 305 | Dic3 | #492 | 1 | 2 | yes | — |
| 306 | C23 | — | 3 | 1 | no | — |
| 307 | C23 | — | 4 | 1 | no | — |
| 308 | C23 | — | 12 | 1 | no | — |
| 309 | Q8 | — | 4 | 2 | no | — |
| 310 | Q8 | — | 4 | 4 | no | — |
| 311 | Q8 | — | 12 | 2 | no | — |
| 312 | Q8 | — | 12 | 4 | no | — |
| 313 | D4 | — | 4 | 2 | no | — |
| 314 | D4 | — | 4 | 4 | no | — |
| 315 | D4 | — | 12 | 2 | no | — |
| 316 | D4 | — | 12 | 4 | no | — |
| 317 | D4 | — | 24 | 2 | no | — |
| 318 | D4 | — | 24 | 2 | no | — |
| 319 | C2×C4 | — | 3 | 1 | no | — |
| 320 | C2×C4 | — | 3 | 4 | no | — |
| 321 | C2×C4 | — | 3 | 2 | no | — |
| 322 | C2×C4 | — | 4 | 2 | no | — |
| 323 | C2×C4 | — | 4 | 1 | no | — |
| 324 | C2×C4 | — | 6 | 4 | no | — |
| 325 | C2×C4 | — | 12 | 2 | no | — |
| 326 | C2×C4 | — | 12 | 1 | no | — |
| 327 | C2×C4 | — | 24 | 2 | no | — |
| 328 | C2×C4 | — | 24 | 2 | no | — |
| 329 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 330 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 331 | C8 | — | 2 | 4 | no | — |
| 332 | C8 | — | 3 | 4 | no | — |
| 333 | C8 | — | 3 | 8 | no | — |
| 334 | C8 | D3×SD16 | 1 | 4 | yes | — |
| 335 | C2×C3 | — | 16 | 1 | no | — |
| 336 | C2×C3 | C2×#492 | 1 | 1 | yes | characteristic |
| 337 | C2×C3 | #3147 | 1 | 2 | yes | — |
| 338 | D3 | — | 2 | 2 | no | — |
| 339 | D3 | — | 16 | 1 | no | — |
| 340 | C22 | — | 3 | 2 | no | — |
| 341 | C22 | — | 6 | 2 | no | — |
| 342 | C22 | — | 8 | 1 | no | — |
| 343 | C22 | — | 8 | 2 | no | — |
| 344 | C22 | — | 24 | 1 | no | — |
| 345 | C22 | — | 24 | 2 | no | — |
| 346 | C22 | D3×#127 | 1 | 1 | yes | characteristic |
| 347 | C4 | — | 3 | 2 | no | — |
| 348 | C4 | — | 6 | 2 | no | — |
| 349 | C4 | — | 8 | 1 | no | — |
| 350 | C4 | — | 8 | 2 | no | — |
| 351 | C4 | — | 24 | 1 | no | — |
| 352 | C4 | — | 24 | 2 | no | — |
| 353 | C4 | C2×D3×SD16 | 1 | 2 | yes | — |
| 354 | C4 | D3×#135 | 1 | 4 | yes | — |
| 355 | C3 | #19596 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 356 | C2 | — | 6 | 2 | no | — |
| 357 | C2 | — | 16 | 1 | no | — |
| 358 | C2 | — | 48 | 1 | no | — |
| 359 | C2 | D3×#492 | 1 | 1 | yes | characteristic |
| 360 | C2 | #81820 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #81891 | C2 | semidirect |
| 3. #81592 | C2 | semidirect |
| 4. #81556 | C2 | semidirect |
| 5. C3×#1708 | C2 | semidirect |
| 6. #71332 | C2 | semidirect |
| 7. #71254 | C2 | semidirect |
| 8. #71212 | C2 | semidirect |
| 9. #71180 | C2 | semidirect |
| 10. #68059 | C2 | semidirect |
| 11. D3×C82 | C2 | semidirect |
| 49. #1708 | D3 | semidirect |
| 173. D3×C8 | SD16 | semidirect |
| 247. C3⋊C8 | #135 | semidirect |
| 355. C3 | #19596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #81891 | 2 |
| #81760 | 2 |
| #81592 | 2 |
| #81556 | 2 |
| C3×#1708 | 2 |
| #71332 | 2 |
| #71254 | 2 |
| #71212 | 2 |
| #71180 | 2 |
| #68059 | 2 |
| D3×C82 | 2 |
| #19596 | 3 |