Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1402 conjugacy classes of subgroups.
The subgroup lattice has 370 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #85725 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #82269 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #82269 | C2 | 1 | 2 | yes | maximal |
| 4 | C3×#1740 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #71593 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #68971 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #23469 | — | 3 | 1 | no | maximal, Sylow |
| 8 | C23×D12 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×C3×#117 | C22 | 1 | 2 | yes | — |
| 10 | C2×C3×#117 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#926 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#926 | C22 | 1 | 2 | yes | — |
| 13 | #5519 | — | 2 | 4 | no | — |
| 14 | #5517 | — | 2 | 4 | no | — |
| 15 | #5500 | — | 2 | 2 | no | — |
| 16 | #5483 | C22 | 1 | 4 | yes | — |
| 17 | #5470 | — | 2 | 2 | no | — |
| 18 | #4988 | — | 2 | 2 | no | — |
| 19 | #4988 | — | 2 | 4 | no | — |
| 20 | #4955 | C22 | 1 | 4 | yes | — |
| 21 | #4955 | C22 | 1 | 8 | yes | — |
| 22 | #4939 | — | 2 | 2 | no | — |
| 23 | #4939 | — | 2 | 4 | no | — |
| 24 | C3×#342 | C22 | 1 | 4 | yes | — |
| 25 | #4527 | C22 | 1 | 8 | yes | — |
| 26 | #3458 | — | 3 | 1 | no | — |
| 27 | #2309 | — | 3 | 2 | no | — |
| 28 | #2309 | — | 3 | 1 | no | — |
| 29 | #2029 | — | 3 | 8 | no | — |
| 30 | #1740 | — | 3 | 2 | no | — |
| 31 | #1740 | D3 | 1 | 1 | yes | characteristic, complemented |
| 32 | C24×D3 | C23 | 1 | 2 | yes | — |
| 33 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 34 | C22×D12 | — | 2 | 1 | no | — |
| 35 | C22×D12 | — | 2 | 2 | no | — |
| 36 | C22×D12 | — | 2 | 1 | no | — |
| 37 | C22×D12 | — | 2 | 2 | no | — |
| 38 | C22×D12 | — | 2 | 4 | no | — |
| 39 | C22×D12 | — | 2 | 2 | no | — |
| 40 | C22×D12 | Q8 | 1 | 4 | yes | complemented |
| 41 | C3×#117 | — | 2 | 2 | no | — |
| 42 | C3×#117 | — | 2 | 2 | no | — |
| 43 | C3×#117 | — | 2 | 4 | no | — |
| 44 | C3×#117 | — | 2 | 4 | no | — |
| 45 | C2×C3×C4⋊C4 | — | 2 | 2 | no | — |
| 46 | C2×C3×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 47 | C2×C3×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 48 | C2×C3×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 49 | C2×C3×C42 | — | 2 | 2 | no | — |
| 50 | C2×C3×C42 | D4 | 1 | 2 | yes | — |
| 51 | C2×#217 | C23 | 1 | 2 | yes | — |
| 52 | C2×#217 | C23 | 1 | 4 | yes | — |
| 53 | C2×(C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 54 | C2×(C2×D3)⋊C4 | — | 2 | 16 | no | — |
| 55 | #926 | — | 2 | 2 | no | — |
| 56 | #926 | — | 2 | 2 | no | — |
| 57 | #926 | — | 2 | 2 | no | — |
| 58 | #926 | — | 2 | 2 | no | — |
| 59 | #926 | — | 2 | 4 | no | — |
| 60 | C2×C4⋊Dic3 | — | 2 | 1 | no | — |
| 61 | C2×C4⋊Dic3 | D4 | 1 | 4 | yes | — |
| 62 | #924 | — | 2 | 8 | no | — |
| 63 | C2×C4×Dic3 | — | 2 | 1 | no | — |
| 64 | C2×C4×Dic3 | D4 | 1 | 4 | yes | — |
| 65 | #890 | — | 2 | 8 | no | — |
| 66 | #888 | — | 2 | 8 | no | — |
| 67 | #878 | — | 2 | 16 | no | — |
| 68 | #870 | — | 2 | 4 | no | — |
| 69 | #869 | — | 2 | 4 | no | — |
| 70 | C4×Dic6 | — | 2 | 8 | no | — |
| 71 | C23×D4 | — | 3 | 1 | no | — |
| 72 | #544 | — | 6 | 4 | no | — |
| 73 | #544 | — | 6 | 2 | no | — |
| 74 | #543 | — | 3 | 4 | no | — |
| 75 | #533 | — | 6 | 4 | no | — |
| 76 | #533 | — | 6 | 2 | no | — |
| 77 | C2×#117 | — | 3 | 2 | no | — |
| 78 | C2×#117 | — | 3 | 1 | no | — |
| 79 | C2×#117 | C2×D3 | 1 | 2 | yes | — |
| 80 | C2×#117 | C2×D3 | 1 | 1 | yes | characteristic |
| 81 | #390 | — | 6 | 4 | no | — |
| 82 | #390 | — | 6 | 4 | no | — |
| 83 | #390 | — | 6 | 2 | no | — |
| 84 | #390 | — | 6 | 2 | no | — |
| 85 | #379 | — | 3 | 8 | no | — |
| 86 | #379 | — | 3 | 4 | no | — |
| 87 | #342 | — | 3 | 8 | no | — |
| 88 | #342 | C2×D3 | 1 | 4 | yes | — |
| 89 | C24×C3 | C24 | 1 | 1 | yes | characteristic |
| 90 | C23×D3 | — | 2 | 2 | no | — |
| 91 | C23×D3 | — | 2 | 4 | no | — |
| 92 | C23×D3 | — | 2 | 4 | no | — |
| 93 | C23×D3 | — | 2 | 2 | no | — |
| 94 | C23×D3 | — | 8 | 4 | no | — |
| 95 | C23×D3 | C2×Q8 | 1 | 4 | yes | — |
| 96 | C22×C3×C4 | — | 2 | 4 | no | — |
| 97 | C22×C3×C4 | C2×D4 | 1 | 4 | yes | — |
| 98 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 101 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 102 | C22×C3×C4 | C2×Q8 | 1 | 2 | yes | — |
| 103 | C22×C3×C4 | #41 | 1 | 4 | yes | — |
| 104 | C22×C3×C4 | #41 | 1 | 2 | yes | — |
| 105 | C22×Dic3 | — | 2 | 2 | no | — |
| 106 | C22×Dic3 | C2×D4 | 1 | 8 | yes | — |
| 107 | C2×D12 | — | 2 | 8 | no | — |
| 108 | C2×D12 | — | 2 | 8 | no | — |
| 109 | C2×D12 | — | 2 | 4 | no | — |
| 110 | C2×D12 | — | 2 | 4 | no | — |
| 111 | C2×D12 | — | 4 | 1 | no | — |
| 112 | C2×D12 | — | 4 | 2 | no | — |
| 113 | C2×D12 | — | 4 | 1 | no | — |
| 114 | C2×D12 | — | 4 | 2 | no | — |
| 115 | C2×D12 | — | 4 | 2 | no | — |
| 116 | C2×D12 | — | 4 | 4 | no | — |
| 117 | C2×D12 | — | 4 | 4 | no | — |
| 118 | C2×Dic6 | — | 2 | 8 | no | — |
| 119 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 120 | C3×C4⋊C4 | — | 4 | 4 | no | — |
| 121 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 122 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 123 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 124 | C3×C42 | — | 2 | 2 | no | — |
| 125 | C3×C42 | — | 2 | 2 | no | — |
| 126 | C3×C42 | — | 4 | 4 | no | — |
| 127 | #217 | — | 2 | 4 | no | — |
| 128 | #217 | — | 2 | 4 | no | — |
| 129 | #217 | — | 2 | 4 | no | — |
| 130 | (C2×D3)⋊C4 | — | 8 | 16 | no | — |
| 131 | (C2×D3)⋊C4 | — | 8 | 8 | no | — |
| 132 | C4⋊Dic3 | — | 2 | 8 | no | — |
| 133 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 134 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 135 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 136 | Dic3⋊C4 | — | 2 | 16 | no | — |
| 137 | C4×Dic3 | — | 2 | 4 | no | — |
| 138 | C4×Dic3 | — | 2 | 4 | no | — |
| 139 | C4×Dic3 | — | 4 | 2 | no | — |
| 140 | C25 | — | 3 | 2 | no | — |
| 141 | C22×D4 | — | 3 | 4 | no | — |
| 142 | C22×D4 | — | 6 | 1 | no | — |
| 143 | C22×D4 | — | 6 | 1 | no | — |
| 144 | C22×D4 | — | 6 | 4 | no | — |
| 145 | C22×D4 | — | 6 | 2 | no | — |
| 146 | C22×D4 | — | 6 | 2 | no | — |
| 147 | C22×D4 | — | 6 | 2 | no | — |
| 148 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 149 | C4⋊Q8 | — | 6 | 4 | no | — |
| 150 | C4⋊Q8 | — | 6 | 8 | no | — |
| 151 | #125 | — | 6 | 4 | no | — |
| 152 | #125 | — | 6 | 8 | no | — |
| 153 | C22⋊Q8 | — | 6 | 16 | no | — |
| 154 | C22⋊Q8 | — | 6 | 8 | no | — |
| 155 | C4×Q8 | — | 6 | 8 | no | — |
| 156 | #117 | — | 2 | 2 | no | — |
| 157 | #117 | — | 2 | 2 | no | — |
| 158 | #117 | — | 2 | 4 | no | — |
| 159 | #117 | — | 2 | 4 | no | — |
| 160 | #117 | — | 6 | 2 | no | — |
| 161 | #117 | — | 6 | 2 | no | — |
| 162 | #117 | — | 6 | 2 | no | — |
| 163 | #117 | — | 6 | 2 | no | — |
| 164 | #117 | — | 6 | 4 | no | — |
| 165 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 166 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 167 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 168 | C2×C4⋊C4 | D12 | 1 | 2 | yes | — |
| 169 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 170 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 171 | C2×C22⋊C4 | — | 6 | 16 | no | — |
| 172 | C2×C22⋊C4 | — | 6 | 8 | no | — |
| 173 | C2×C22⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 174 | C2×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 175 | C2×C42 | — | 2 | 2 | no | — |
| 176 | C2×C42 | — | 3 | 4 | no | — |
| 177 | C2×C42 | — | 6 | 1 | no | — |
| 178 | C2×C42 | D12 | 1 | 2 | yes | — |
| 179 | C23×C3 | — | 4 | 2 | no | — |
| 180 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 181 | C23×C3 | C22×D4 | 1 | 2 | yes | — |
| 182 | C23×C3 | C22×Q8 | 1 | 1 | yes | characteristic |
| 183 | C23×C3 | C2×#41 | 1 | 2 | yes | — |
| 184 | C23×C3 | C2×#41 | 1 | 1 | yes | characteristic |
| 185 | C22×D3 | — | 2 | 8 | no | — |
| 186 | C22×D3 | — | 2 | 4 | no | — |
| 187 | C22×D3 | — | 4 | 8 | no | — |
| 188 | C22×D3 | — | 4 | 16 | no | — |
| 189 | C22×D3 | — | 4 | 2 | no | — |
| 190 | C22×D3 | — | 4 | 2 | no | — |
| 191 | C22×D3 | — | 4 | 4 | no | — |
| 192 | C22×D3 | — | 8 | 4 | no | — |
| 193 | C22×D3 | — | 8 | 8 | no | — |
| 194 | C22×D3 | — | 8 | 4 | no | — |
| 195 | C2×C3×C4 | — | 2 | 4 | no | — |
| 196 | C2×C3×C4 | — | 4 | 4 | no | — |
| 197 | C2×C3×C4 | — | 4 | 8 | no | — |
| 198 | C2×C3×C4 | — | 4 | 4 | no | — |
| 199 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 200 | C2×C3×C4 | #120 | 1 | 2 | yes | — |
| 201 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 202 | C2×C3×C4 | C22⋊Q8 | 1 | 4 | yes | — |
| 203 | C2×C3×C4 | C22⋊Q8 | 1 | 4 | yes | — |
| 204 | C2×C3×C4 | C22⋊Q8 | 1 | 2 | yes | — |
| 205 | C2×C3×C4 | C22⋊Q8 | 1 | 2 | yes | — |
| 206 | C2×C3×C4 | #124 | 1 | 2 | yes | — |
| 207 | C2×C3×C4 | #124 | 1 | 2 | yes | — |
| 208 | C2×C3×C4 | #124 | 1 | 4 | yes | — |
| 209 | C2×C3×C4 | #124 | 1 | 4 | yes | — |
| 210 | C2×Dic3 | — | 2 | 8 | no | — |
| 211 | C2×Dic3 | — | 4 | 8 | no | — |
| 212 | C2×Dic3 | — | 4 | 4 | no | — |
| 213 | C2×Dic3 | — | 4 | 2 | no | — |
| 214 | D12 | — | 4 | 4 | no | — |
| 215 | D12 | — | 4 | 8 | no | — |
| 216 | D12 | — | 4 | 4 | no | — |
| 217 | Dic6 | — | 8 | 8 | no | — |
| 218 | C24 | — | 3 | 4 | no | — |
| 219 | C24 | — | 6 | 2 | no | — |
| 220 | C24 | — | 6 | 4 | no | — |
| 221 | C24 | — | 6 | 4 | no | — |
| 222 | C24 | — | 6 | 2 | no | — |
| 223 | C24 | — | 24 | 4 | no | — |
| 224 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 225 | C2×Q8 | — | 6 | 8 | no | — |
| 226 | C2×D4 | — | 6 | 8 | no | — |
| 227 | C2×D4 | — | 6 | 8 | no | — |
| 228 | C2×D4 | — | 6 | 4 | no | — |
| 229 | C2×D4 | — | 6 | 4 | no | — |
| 230 | C2×D4 | — | 12 | 2 | no | — |
| 231 | C2×D4 | — | 12 | 2 | no | — |
| 232 | C2×D4 | — | 12 | 1 | no | — |
| 233 | C2×D4 | — | 12 | 1 | no | — |
| 234 | C2×D4 | — | 12 | 2 | no | — |
| 235 | C2×D4 | — | 12 | 4 | no | — |
| 236 | C2×D4 | — | 12 | 4 | no | — |
| 237 | C22×C4 | — | 2 | 4 | no | — |
| 238 | C22×C4 | — | 3 | 8 | no | — |
| 239 | C22×C4 | — | 6 | 2 | no | — |
| 240 | C22×C4 | C2×D12 | 1 | 4 | yes | — |
| 241 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 242 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 243 | C22×C4 | #235 | 1 | 4 | yes | — |
| 244 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 245 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 246 | C22×C4 | #237 | 1 | 2 | yes | — |
| 247 | C22×C4 | D3×Q8 | 1 | 2 | yes | — |
| 248 | C4⋊C4 | — | 2 | 4 | no | — |
| 249 | C4⋊C4 | — | 4 | 4 | no | — |
| 250 | C4⋊C4 | — | 6 | 16 | no | — |
| 251 | C4⋊C4 | — | 6 | 8 | no | — |
| 252 | C4⋊C4 | — | 6 | 4 | no | — |
| 253 | C4⋊C4 | — | 6 | 4 | no | — |
| 254 | C4⋊C4 | — | 12 | 2 | no | — |
| 255 | C22⋊C4 | — | 2 | 4 | no | — |
| 256 | C22⋊C4 | — | 2 | 4 | no | — |
| 257 | C22⋊C4 | — | 2 | 4 | no | — |
| 258 | C22⋊C4 | — | 6 | 4 | no | — |
| 259 | C22⋊C4 | — | 6 | 4 | no | — |
| 260 | C22⋊C4 | — | 6 | 4 | no | — |
| 261 | C22⋊C4 | — | 24 | 8 | no | — |
| 262 | C22⋊C4 | — | 24 | 16 | no | — |
| 263 | C42 | — | 2 | 2 | no | — |
| 264 | C42 | — | 2 | 2 | no | — |
| 265 | C42 | — | 4 | 4 | no | — |
| 266 | C42 | — | 6 | 4 | no | — |
| 267 | C42 | — | 6 | 4 | no | — |
| 268 | C42 | — | 12 | 2 | no | — |
| 269 | C22×C3 | — | 2 | 2 | no | — |
| 270 | C22×C3 | — | 2 | 4 | no | — |
| 271 | C22×C3 | — | 4 | 1 | no | — |
| 272 | C22×C3 | — | 4 | 2 | no | — |
| 273 | C22×C3 | — | 4 | 1 | no | — |
| 274 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 275 | C22×C3 | C2×C22⋊Q8 | 1 | 2 | yes | — |
| 276 | C22×C3 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 277 | C22×C3 | C2×#124 | 1 | 1 | yes | characteristic |
| 278 | C22×C3 | C2×#124 | 1 | 2 | yes | — |
| 279 | C2×D3 | — | 4 | 16 | no | — |
| 280 | C2×D3 | — | 4 | 8 | no | — |
| 281 | C2×D3 | — | 4 | 4 | no | — |
| 282 | C2×D3 | — | 8 | 4 | no | — |
| 283 | C2×D3 | — | 8 | 8 | no | — |
| 284 | C2×D3 | — | 8 | 4 | no | — |
| 285 | C3×C4 | — | 4 | 4 | no | — |
| 286 | C3×C4 | — | 8 | 4 | no | — |
| 287 | C3×C4 | #393 | 1 | 2 | yes | — |
| 288 | C3×C4 | #393 | 1 | 4 | yes | — |
| 289 | C3×C4 | #393 | 1 | 2 | yes | — |
| 290 | Dic3 | — | 4 | 8 | no | — |
| 291 | Dic3 | — | 8 | 2 | no | — |
| 292 | C23 | — | 4 | 2 | no | — |
| 293 | C23 | — | 6 | 8 | no | — |
| 294 | C23 | — | 6 | 4 | no | — |
| 295 | C23 | — | 12 | 8 | no | — |
| 296 | C23 | — | 12 | 16 | no | — |
| 297 | C23 | — | 12 | 2 | no | — |
| 298 | C23 | — | 12 | 2 | no | — |
| 299 | C23 | — | 12 | 4 | no | — |
| 300 | C23 | — | 24 | 4 | no | — |
| 301 | C23 | — | 24 | 8 | no | — |
| 302 | C23 | — | 24 | 4 | no | — |
| 303 | C23 | C22×D12 | 1 | 1 | yes | characteristic |
| 304 | C23 | C2×#235 | 1 | 2 | yes | — |
| 305 | C23 | C2×D3×D4 | 1 | 2 | yes | — |
| 306 | C23 | C2×#237 | 1 | 1 | yes | characteristic |
| 307 | C23 | C2×D3×Q8 | 1 | 1 | yes | characteristic |
| 308 | Q8 | — | 24 | 8 | no | — |
| 309 | D4 | — | 12 | 8 | no | — |
| 310 | D4 | — | 12 | 4 | no | — |
| 311 | D4 | — | 12 | 4 | no | — |
| 312 | C2×C4 | — | 2 | 4 | no | — |
| 313 | C2×C4 | — | 4 | 4 | no | — |
| 314 | C2×C4 | — | 4 | 8 | no | — |
| 315 | C2×C4 | — | 4 | 4 | no | — |
| 316 | C2×C4 | — | 6 | 8 | no | — |
| 317 | C2×C4 | — | 12 | 8 | no | — |
| 318 | C2×C4 | — | 12 | 4 | no | — |
| 319 | C2×C4 | — | 12 | 2 | no | — |
| 320 | C2×C4 | #875 | 1 | 2 | yes | — |
| 321 | C2×C4 | #875 | 1 | 2 | yes | — |
| 322 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 323 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 324 | C2×C4 | #882 | 1 | 2 | yes | — |
| 325 | C2×C4 | #885 | 1 | 4 | yes | — |
| 326 | C2×C4 | #885 | 1 | 4 | yes | — |
| 327 | C2×C4 | #896 | 1 | 4 | yes | — |
| 328 | C2×C4 | #896 | 1 | 4 | yes | — |
| 329 | C2×C4 | #897 | 1 | 2 | yes | — |
| 330 | C2×C4 | #897 | 1 | 2 | yes | — |
| 331 | C2×C3 | — | 2 | 1 | no | — |
| 332 | C2×C3 | — | 2 | 2 | no | — |
| 333 | C2×C3 | — | 2 | 2 | no | — |
| 334 | C2×C3 | — | 2 | 1 | no | — |
| 335 | C2×C3 | C2×#393 | 1 | 1 | yes | characteristic |
| 336 | C2×C3 | #3027 | 1 | 2 | yes | — |
| 337 | D3 | — | 8 | 4 | no | — |
| 338 | C22 | — | 2 | 2 | no | — |
| 339 | C22 | — | 2 | 4 | no | — |
| 340 | C22 | — | 4 | 2 | no | — |
| 341 | C22 | — | 4 | 1 | no | — |
| 342 | C22 | — | 4 | 1 | no | — |
| 343 | C22 | — | 12 | 16 | no | — |
| 344 | C22 | — | 12 | 8 | no | — |
| 345 | C22 | — | 12 | 4 | no | — |
| 346 | C22 | — | 24 | 8 | no | — |
| 347 | C22 | — | 24 | 4 | no | — |
| 348 | C22 | — | 24 | 4 | no | — |
| 349 | C22 | C2×#875 | 1 | 1 | yes | characteristic |
| 350 | C22 | C2×#882 | 1 | 1 | yes | characteristic |
| 351 | C22 | C2×#885 | 1 | 2 | yes | — |
| 352 | C22 | C2×#896 | 1 | 2 | yes | — |
| 353 | C22 | C2×#897 | 1 | 1 | yes | characteristic |
| 354 | C4 | — | 4 | 4 | no | — |
| 355 | C4 | — | 8 | 4 | no | — |
| 356 | C4 | — | 12 | 8 | no | — |
| 357 | C4 | — | 24 | 2 | no | — |
| 358 | C4 | #4673 | 1 | 4 | yes | — |
| 359 | C4 | #4673 | 1 | 2 | yes | — |
| 360 | C4 | #4673 | 1 | 2 | yes | — |
| 361 | C3 | #23469 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 362 | C2 | — | 2 | 2 | no | — |
| 363 | C2 | — | 2 | 1 | no | — |
| 364 | C2 | — | 2 | 2 | no | — |
| 365 | C2 | — | 2 | 1 | no | — |
| 366 | C2 | — | 24 | 4 | no | — |
| 367 | C2 | C2×#4673 | 1 | 1 | yes | characteristic |
| 368 | C2 | #78691 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #85725 | C2 | semidirect |
| 4. C3×#1740 | C2 | semidirect |
| 5. #71593 | C2 | semidirect |
| 6. #68971 | C2 | semidirect |
| 31. #1740 | D3 | semidirect |
| 40. C22×D12 | Q8 | semidirect |
| 361. C3 | #23469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #85725 | 2 |
| #82269 | 2 |
| C3×#1740 | 2 |
| #71593 | 2 |
| #68971 | 2 |
| #23469 | 3 |