Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
662 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 115 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 | C3×#2379 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5058 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#4540 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #69553 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #67630 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #9001 | — | 3 | 1 | no | maximal, Sylow |
| 7 | C2×C3×#124 | C22 | 1 | 1 | yes | characteristic |
| 8 | C22×#215 | — | 2 | 1 | no | — |
| 9 | C22×#213 | — | 2 | 1 | no | — |
| 10 | C2×#874 | C22 | 1 | 1 | yes | characteristic |
| 11 | C3×#391 | — | 2 | 1 | no | — |
| 12 | C3×#388 | — | 2 | 2 | no | — |
| 13 | C3×#386 | — | 2 | 1 | no | — |
| 14 | C3×#385 | — | 2 | 2 | no | — |
| 15 | C3×#382 | C22 | 1 | 2 | yes | — |
| 16 | #5058 | — | 2 | 2 | no | — |
| 17 | #5058 | C4 | 1 | 4 | yes | complemented |
| 18 | C2×#809 | — | 2 | 2 | no | — |
| 19 | C2×#809 | — | 2 | 2 | no | — |
| 20 | C2×#803 | C22 | 1 | 2 | yes | — |
| 21 | C2×#803 | C22 | 1 | 1 | yes | characteristic |
| 22 | #4540 | — | 2 | 2 | no | — |
| 23 | C2×#496 | — | 3 | 1 | no | — |
| 24 | #2379 | D3 | 1 | 1 | yes | characteristic, complemented |
| 25 | #1961 | — | 3 | 2 | no | — |
| 26 | C2×#329 | — | 3 | 1 | no | — |
| 27 | #1295 | — | 3 | 2 | no | — |
| 28 | C22×C3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 29 | C22×C3×D4 | D4 | 1 | 1 | yes | characteristic |
| 30 | C23×C3×C4 | — | 2 | 1 | no | — |
| 31 | C22×D12 | — | 2 | 2 | no | — |
| 32 | C22×D12 | — | 2 | 1 | no | — |
| 33 | C3×#124 | — | 2 | 2 | no | — |
| 34 | C3×#124 | C2×C4 | 1 | 2 | yes | — |
| 35 | C3×#124 | D4 | 1 | 2 | yes | — |
| 36 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 37 | C2×C3×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 38 | C2×C3×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 39 | C2×C3×C22⋊C4 | — | 2 | 2 | no | — |
| 40 | C2×C3×C22⋊C4 | — | 2 | 2 | no | — |
| 41 | C2×C3×C22⋊C4 | — | 2 | 1 | no | — |
| 42 | C2×C3×C42 | — | 2 | 1 | no | — |
| 43 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 44 | C2×#215 | — | 2 | 4 | no | — |
| 45 | C2×#215 | — | 4 | 2 | no | — |
| 46 | C2×#215 | — | 4 | 2 | no | — |
| 47 | C2×#213 | — | 2 | 4 | no | — |
| 48 | C2×#213 | — | 4 | 2 | no | — |
| 49 | C2×#213 | — | 4 | 2 | no | — |
| 50 | C22×C3⋊C8 | — | 2 | 1 | no | — |
| 51 | C22×C3⋊C8 | — | 2 | 2 | no | — |
| 52 | #874 | — | 2 | 1 | no | — |
| 53 | #874 | — | 2 | 2 | no | — |
| 54 | #874 | C2×C4 | 1 | 2 | yes | complemented |
| 55 | C3×#95 | — | 2 | 2 | no | — |
| 56 | C3×#95 | — | 2 | 2 | no | — |
| 57 | C3×#95 | — | 2 | 2 | no | — |
| 58 | #809 | — | 4 | 4 | no | — |
| 59 | #809 | — | 4 | 4 | no | — |
| 60 | #803 | — | 2 | 1 | no | — |
| 61 | #803 | — | 2 | 2 | no | — |
| 62 | #803 | — | 2 | 2 | no | — |
| 63 | #803 | C2×C4 | 1 | 2 | yes | complemented |
| 64 | C22×SD16 | — | 6 | 1 | no | — |
| 65 | C22×D8 | — | 6 | 1 | no | — |
| 66 | C2×#127 | — | 3 | 1 | no | — |
| 67 | C2×#124 | C2×D3 | 1 | 1 | yes | characteristic |
| 68 | #496 | — | 3 | 4 | no | — |
| 69 | #496 | — | 6 | 2 | no | — |
| 70 | C2×#102 | — | 6 | 2 | no | — |
| 71 | C2×#102 | — | 6 | 2 | no | — |
| 72 | C2×#97 | — | 3 | 1 | no | — |
| 73 | C2×#97 | — | 3 | 2 | no | — |
| 74 | #391 | — | 2 | 1 | no | — |
| 75 | #388 | — | 2 | 2 | no | — |
| 76 | #386 | — | 2 | 1 | no | — |
| 77 | #385 | — | 2 | 2 | no | — |
| 78 | #382 | C2×D3 | 1 | 2 | yes | — |
| 79 | #329 | — | 6 | 2 | no | — |
| 80 | C24×C3 | — | 2 | 1 | no | — |
| 81 | C23×D3 | — | 4 | 1 | no | — |
| 82 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 83 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 84 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 85 | C2×C3×Q8 | C22⋊C4 | 1 | 2 | yes | — |
| 86 | C2×C3×D4 | — | 2 | 1 | no | — |
| 87 | C2×C3×D4 | — | 4 | 1 | no | — |
| 88 | C2×C3×D4 | — | 4 | 1 | no | — |
| 89 | C2×C3×D4 | C22⋊C4 | 1 | 2 | yes | — |
| 90 | C22×C3×C4 | — | 2 | 1 | no | — |
| 91 | C22×C3×C4 | — | 2 | 2 | no | — |
| 92 | C22×C3×C4 | — | 2 | 2 | no | — |
| 93 | C22×C3×C4 | — | 8 | 2 | no | — |
| 94 | C22×C3×C4 | — | 8 | 1 | no | — |
| 95 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 97 | C2×D12 | — | 2 | 2 | no | — |
| 98 | C2×D12 | — | 2 | 4 | no | — |
| 99 | C2×D12 | — | 4 | 2 | no | — |
| 100 | C2×D12 | — | 4 | 2 | no | — |
| 101 | C2×D12 | — | 4 | 1 | no | — |
| 102 | C2×D12 | — | 4 | 1 | no | — |
| 103 | C2×D12 | — | 4 | 1 | no | — |
| 104 | C2×D12 | — | 4 | 1 | no | — |
| 105 | C2×D12 | — | 4 | 2 | no | — |
| 106 | C2×D12 | — | 4 | 2 | no | — |
| 107 | C2×D12 | — | 4 | 2 | no | — |
| 108 | C2×D12 | — | 4 | 1 | no | — |
| 109 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 110 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 111 | C3×C4⋊C4 | — | 8 | 1 | no | — |
| 112 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 113 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 114 | C3×C22⋊C4 | — | 8 | 1 | no | — |
| 115 | C3×C22⋊C4 | — | 8 | 2 | no | — |
| 116 | C3×C42 | — | 8 | 1 | no | — |
| 117 | C3×C42 | C22×C4 | 1 | 1 | yes | characteristic |
| 118 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C3×C42 | #41 | 1 | 2 | yes | — |
| 120 | #215 | — | 4 | 8 | no | — |
| 121 | #213 | — | 4 | 8 | no | — |
| 122 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 123 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 124 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 125 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 126 | C2×C3⋊C8 | — | 4 | 2 | no | — |
| 127 | C2×C3⋊C8 | — | 4 | 2 | no | — |
| 128 | C22×Q8 | #67 | 1 | 1 | yes | characteristic |
| 129 | C22×D4 | — | 6 | 1 | no | — |
| 130 | C22×D4 | — | 6 | 2 | no | — |
| 131 | C22×D4 | #67 | 1 | 1 | yes | characteristic |
| 132 | C23×C4 | — | 2 | 1 | no | — |
| 133 | C2×SD16 | — | 6 | 4 | no | — |
| 134 | C2×SD16 | — | 12 | 2 | no | — |
| 135 | C2×SD16 | — | 12 | 2 | no | — |
| 136 | C2×D8 | — | 6 | 4 | no | — |
| 137 | C2×D8 | — | 12 | 2 | no | — |
| 138 | C2×D8 | — | 12 | 2 | no | — |
| 139 | C22×C8 | — | 6 | 1 | no | — |
| 140 | C22×C8 | — | 6 | 2 | no | — |
| 141 | #127 | — | 3 | 2 | no | — |
| 142 | #127 | — | 6 | 1 | no | — |
| 143 | #127 | — | 6 | 2 | no | — |
| 144 | #124 | — | 2 | 2 | no | — |
| 145 | #124 | C4×D3 | 1 | 2 | yes | — |
| 146 | #124 | D12 | 1 | 2 | yes | — |
| 147 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 148 | C2×C4⋊C4 | #67 | 1 | 2 | yes | — |
| 149 | C2×C4⋊C4 | #67 | 1 | 2 | yes | — |
| 150 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 151 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 152 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 153 | C2×C42 | — | 2 | 1 | no | — |
| 154 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 155 | #102 | — | 12 | 4 | no | — |
| 156 | #102 | — | 12 | 4 | no | — |
| 157 | #97 | — | 3 | 2 | no | — |
| 158 | #97 | — | 6 | 1 | no | — |
| 159 | #97 | — | 6 | 2 | no | — |
| 160 | #97 | — | 6 | 2 | no | — |
| 161 | #95 | — | 2 | 2 | no | — |
| 162 | #95 | — | 2 | 2 | no | — |
| 163 | #95 | — | 2 | 2 | no | — |
| 164 | C23×C3 | — | 2 | 2 | no | — |
| 165 | C23×C3 | — | 4 | 2 | no | — |
| 166 | C23×C3 | — | 4 | 1 | no | — |
| 167 | C23×C3 | — | 4 | 1 | no | — |
| 168 | C23×C3 | — | 4 | 2 | no | — |
| 169 | C23×C3 | #120 | 1 | 1 | yes | characteristic |
| 170 | C22×D3 | — | 4 | 2 | no | — |
| 171 | C22×D3 | — | 8 | 2 | no | — |
| 172 | C22×D3 | — | 8 | 1 | no | — |
| 173 | C22×D3 | — | 8 | 1 | no | — |
| 174 | C22×D3 | — | 8 | 2 | no | — |
| 175 | C3×Q8 | — | 4 | 2 | no | — |
| 176 | C3×Q8 | — | 8 | 1 | no | — |
| 177 | C3×D4 | — | 4 | 2 | no | — |
| 178 | C3×D4 | — | 8 | 1 | no | — |
| 179 | C2×C3×C4 | — | 2 | 2 | no | — |
| 180 | C2×C3×C4 | — | 2 | 1 | no | — |
| 181 | C2×C3×C4 | — | 2 | 1 | no | — |
| 182 | C2×C3×C4 | — | 2 | 2 | no | — |
| 183 | C2×C3×C4 | — | 2 | 2 | no | — |
| 184 | C2×C3×C4 | — | 4 | 1 | no | — |
| 185 | C2×C3×C4 | — | 4 | 1 | no | — |
| 186 | C2×C3×C4 | — | 4 | 2 | no | — |
| 187 | C2×C3×C4 | — | 4 | 2 | no | — |
| 188 | C2×C3×C4 | — | 4 | 2 | no | — |
| 189 | C2×C3×C4 | — | 4 | 2 | no | — |
| 190 | C2×C3×C4 | — | 4 | 2 | no | — |
| 191 | C2×C3×C4 | — | 4 | 2 | no | — |
| 192 | C2×C3×C4 | — | 8 | 4 | no | — |
| 193 | C2×C3×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 194 | C2×C3×C4 | C4×D4 | 1 | 2 | yes | — |
| 195 | C2×C3×C4 | #121 | 1 | 2 | yes | — |
| 196 | C2×C3×C4 | #123 | 1 | 1 | yes | characteristic |
| 197 | D12 | — | 4 | 2 | no | — |
| 198 | D12 | — | 4 | 2 | no | — |
| 199 | D12 | — | 4 | 4 | no | — |
| 200 | D12 | — | 4 | 4 | no | — |
| 201 | D12 | — | 8 | 2 | no | — |
| 202 | D12 | — | 8 | 2 | no | — |
| 203 | D12 | — | 8 | 1 | no | — |
| 204 | D12 | — | 8 | 1 | no | — |
| 205 | C3⋊C8 | — | 2 | 4 | no | — |
| 206 | C3⋊C8 | — | 4 | 4 | no | — |
| 207 | C24 | — | 2 | 1 | no | — |
| 208 | C24 | — | 12 | 1 | no | — |
| 209 | C2×Q8 | — | 2 | 1 | no | — |
| 210 | C2×Q8 | — | 4 | 1 | no | — |
| 211 | C2×Q8 | — | 4 | 1 | no | — |
| 212 | C2×Q8 | (C2×D3)⋊C4 | 1 | 2 | yes | — |
| 213 | C2×D4 | — | 2 | 1 | no | — |
| 214 | C2×D4 | — | 4 | 1 | no | — |
| 215 | C2×D4 | — | 4 | 1 | no | — |
| 216 | C2×D4 | — | 6 | 2 | no | — |
| 217 | C2×D4 | — | 6 | 4 | no | — |
| 218 | C2×D4 | — | 12 | 2 | no | — |
| 219 | C2×D4 | — | 12 | 2 | no | — |
| 220 | C2×D4 | — | 12 | 1 | no | — |
| 221 | C2×D4 | — | 12 | 1 | no | — |
| 222 | C2×D4 | — | 12 | 1 | no | — |
| 223 | C2×D4 | — | 12 | 1 | no | — |
| 224 | C2×D4 | — | 12 | 2 | no | — |
| 225 | C2×D4 | — | 12 | 2 | no | — |
| 226 | C2×D4 | — | 12 | 1 | no | — |
| 227 | C2×D4 | — | 12 | 2 | no | — |
| 228 | C2×D4 | (C2×D3)⋊C4 | 1 | 2 | yes | — |
| 229 | C22×C4 | — | 2 | 1 | no | — |
| 230 | C22×C4 | — | 2 | 2 | no | — |
| 231 | C22×C4 | — | 2 | 2 | no | — |
| 232 | C22×C4 | — | 8 | 2 | no | — |
| 233 | C22×C4 | — | 8 | 1 | no | — |
| 234 | C22×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 235 | C22×C4 | C2×#67 | 1 | 2 | yes | — |
| 236 | SD16 | — | 12 | 8 | no | — |
| 237 | D8 | — | 12 | 8 | no | — |
| 238 | C2×C8 | — | 6 | 2 | no | — |
| 239 | C2×C8 | — | 6 | 2 | no | — |
| 240 | C2×C8 | — | 6 | 2 | no | — |
| 241 | C2×C8 | — | 6 | 4 | no | — |
| 242 | C2×C8 | — | 12 | 2 | no | — |
| 243 | C2×C8 | — | 12 | 2 | no | — |
| 244 | C4⋊C4 | — | 4 | 2 | no | — |
| 245 | C4⋊C4 | — | 4 | 2 | no | — |
| 246 | C4⋊C4 | — | 8 | 1 | no | — |
| 247 | C22⋊C4 | — | 2 | 4 | no | — |
| 248 | C22⋊C4 | — | 2 | 4 | no | — |
| 249 | C22⋊C4 | — | 8 | 1 | no | — |
| 250 | C22⋊C4 | — | 8 | 2 | no | — |
| 251 | C42 | — | 8 | 1 | no | — |
| 252 | C42 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 253 | C42 | C2×D12 | 1 | 1 | yes | characteristic |
| 254 | C42 | #235 | 1 | 2 | yes | — |
| 255 | C22×C3 | — | 4 | 4 | no | — |
| 256 | C22×C3 | — | 4 | 2 | no | — |
| 257 | C22×C3 | — | 8 | 1 | no | — |
| 258 | C22×C3 | — | 8 | 2 | no | — |
| 259 | C22×C3 | — | 8 | 1 | no | — |
| 260 | C22×C3 | #386 | 1 | 1 | yes | characteristic |
| 261 | C22×C3 | #453 | 1 | 2 | yes | — |
| 262 | C22×C3 | #453 | 1 | 1 | yes | characteristic |
| 263 | C22×C3 | #453 | 1 | 1 | yes | characteristic |
| 264 | C22×C3 | #454 | 1 | 2 | yes | — |
| 265 | C2×D3 | — | 8 | 4 | no | — |
| 266 | C2×D3 | — | 8 | 2 | no | — |
| 267 | C2×D3 | — | 16 | 1 | no | — |
| 268 | C2×D3 | — | 16 | 2 | no | — |
| 269 | C2×D3 | — | 16 | 1 | no | — |
| 270 | C3×C4 | — | 2 | 2 | no | — |
| 271 | C3×C4 | — | 2 | 2 | no | — |
| 272 | C3×C4 | — | 2 | 1 | no | — |
| 273 | C3×C4 | — | 2 | 1 | no | — |
| 274 | C3×C4 | — | 4 | 2 | no | — |
| 275 | C3×C4 | — | 8 | 2 | no | — |
| 276 | C3×C4 | — | 8 | 2 | no | — |
| 277 | C23 | — | 2 | 2 | no | — |
| 278 | C23 | — | 4 | 2 | no | — |
| 279 | C23 | — | 4 | 1 | no | — |
| 280 | C23 | — | 4 | 1 | no | — |
| 281 | C23 | — | 4 | 2 | no | — |
| 282 | C23 | — | 12 | 2 | no | — |
| 283 | C23 | — | 24 | 1 | no | — |
| 284 | C23 | — | 24 | 1 | no | — |
| 285 | C23 | — | 24 | 2 | no | — |
| 286 | C23 | — | 24 | 2 | no | — |
| 287 | C23 | #953 | 1 | 1 | yes | characteristic |
| 288 | Q8 | — | 4 | 2 | no | — |
| 289 | Q8 | — | 8 | 1 | no | — |
| 290 | D4 | — | 4 | 2 | no | — |
| 291 | D4 | — | 8 | 1 | no | — |
| 292 | D4 | — | 12 | 2 | no | — |
| 293 | D4 | — | 12 | 2 | no | — |
| 294 | D4 | — | 12 | 4 | no | — |
| 295 | D4 | — | 12 | 4 | no | — |
| 296 | D4 | — | 24 | 1 | no | — |
| 297 | D4 | — | 24 | 1 | no | — |
| 298 | D4 | — | 24 | 2 | no | — |
| 299 | D4 | — | 24 | 2 | no | — |
| 300 | C2×C4 | — | 2 | 2 | no | — |
| 301 | C2×C4 | — | 2 | 1 | no | — |
| 302 | C2×C4 | — | 2 | 1 | no | — |
| 303 | C2×C4 | — | 2 | 2 | no | — |
| 304 | C2×C4 | — | 2 | 2 | no | — |
| 305 | C2×C4 | — | 4 | 1 | no | — |
| 306 | C2×C4 | — | 4 | 1 | no | — |
| 307 | C2×C4 | — | 4 | 2 | no | — |
| 308 | C2×C4 | — | 4 | 2 | no | — |
| 309 | C2×C4 | — | 4 | 2 | no | — |
| 310 | C2×C4 | — | 4 | 2 | no | — |
| 311 | C2×C4 | — | 4 | 2 | no | — |
| 312 | C2×C4 | — | 4 | 2 | no | — |
| 313 | C2×C4 | — | 8 | 4 | no | — |
| 314 | C2×C4 | C2×(C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 315 | C2×C4 | C4×#67 | 1 | 2 | yes | — |
| 316 | C2×C4 | #929 | 1 | 1 | yes | characteristic |
| 317 | C2×C4 | #930 | 1 | 2 | yes | — |
| 318 | C8 | — | 6 | 4 | no | — |
| 319 | C8 | — | 12 | 4 | no | — |
| 320 | C2×C3 | — | 8 | 2 | no | — |
| 321 | C2×C3 | #1655 | 1 | 1 | yes | characteristic |
| 322 | C2×C3 | #1656 | 1 | 2 | yes | — |
| 323 | C2×C3 | #1657 | 1 | 1 | yes | characteristic |
| 324 | C2×C3 | #1883 | 1 | 2 | yes | — |
| 325 | C2×C3 | #1887 | 1 | 1 | yes | characteristic |
| 326 | D3 | — | 16 | 2 | no | — |
| 327 | C22 | — | 4 | 2 | no | — |
| 328 | C22 | — | 4 | 4 | no | — |
| 329 | C22 | — | 8 | 1 | no | — |
| 330 | C22 | — | 8 | 2 | no | — |
| 331 | C22 | — | 8 | 1 | no | — |
| 332 | C22 | — | 24 | 2 | no | — |
| 333 | C22 | — | 24 | 4 | no | — |
| 334 | C22 | — | 48 | 1 | no | — |
| 335 | C22 | — | 48 | 2 | no | — |
| 336 | C22 | — | 48 | 1 | no | — |
| 337 | C22 | #5213 | 1 | 1 | yes | characteristic |
| 338 | C22 | #5241 | 1 | 2 | yes | — |
| 339 | C22 | #5241 | 1 | 1 | yes | characteristic |
| 340 | C22 | #5241 | 1 | 1 | yes | characteristic |
| 341 | C22 | #5245 | 1 | 2 | yes | — |
| 342 | C4 | — | 2 | 1 | no | — |
| 343 | C4 | — | 2 | 1 | no | — |
| 344 | C4 | — | 2 | 2 | no | — |
| 345 | C4 | — | 2 | 2 | no | — |
| 346 | C4 | — | 4 | 2 | no | — |
| 347 | C4 | — | 8 | 2 | no | — |
| 348 | C4 | — | 8 | 2 | no | — |
| 349 | C3 | #9001 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 350 | C2 | — | 8 | 2 | no | — |
| 351 | C2 | — | 48 | 2 | no | — |
| 352 | C2 | #71650 | 1 | 1 | yes | characteristic |
| 353 | C2 | #71667 | 1 | 2 | yes | — |
| 354 | C2 | #71948 | 1 | 1 | yes | characteristic |
| 355 | C2 | #71952 | 1 | 2 | yes | — |
| 356 | C2 | #71955 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#2379 | C2 | semidirect |
| 3. C2×#4540 | C2 | semidirect |
| 4. #69553 | C2 | semidirect |
| 5. #67630 | C2 | semidirect |
| 17. #5058 | C4 | semidirect |
| 24. #2379 | D3 | semidirect |
| 54. #874 | C2×C4 | semidirect |
| 63. #803 | C2×C4 | semidirect |
| 349. C3 | #9001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2379 | 2 |
| C2×#5058 | 2 |
| C2×#4540 | 2 |
| #69553 | 2 |
| #67630 | 2 |
| #9001 | 3 |