Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
654 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #79258 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #79070 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#2103 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #70738 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #70547 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #69039 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #69034 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #68947 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #68918 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #68727 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #68716 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #29386 | — | 3 | 1 | no | maximal, Sylow |
| 13 | #5748 | C22 | 1 | 1 | yes | characteristic |
| 14 | #5748 | C22 | 1 | 2 | yes | — |
| 15 | #5745 | C22 | 1 | 2 | yes | — |
| 16 | #5522 | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×#430 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#424 | C22 | 1 | 1 | yes | characteristic |
| 19 | #5139 | C22 | 1 | 2 | yes | — |
| 20 | C2×#825 | C22 | 1 | 2 | yes | — |
| 21 | #5129 | C22 | 1 | 1 | yes | characteristic |
| 22 | #5129 | C22 | 1 | 2 | yes | — |
| 23 | #5119 | C22 | 1 | 2 | yes | — |
| 24 | Dic3×M16 | C22 | 1 | 1 | yes | characteristic |
| 25 | #5113 | C22 | 1 | 2 | yes | — |
| 26 | #5110 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×C8×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 28 | #5006 | C22 | 1 | 2 | yes | — |
| 29 | #4999 | C22 | 1 | 1 | yes | characteristic |
| 30 | #4895 | — | 2 | 2 | no | — |
| 31 | #4894 | — | 2 | 2 | no | — |
| 32 | #4840 | — | 2 | 2 | no | — |
| 33 | #4833 | — | 2 | 2 | no | — |
| 34 | C3×#344 | C22 | 1 | 2 | yes | — |
| 35 | C3×#341 | C22 | 1 | 2 | yes | — |
| 36 | C3×#338 | C22 | 1 | 1 | yes | characteristic |
| 37 | #4559 | C22 | 1 | 2 | yes | — |
| 38 | #4557 | C22 | 1 | 1 | yes | characteristic |
| 39 | #4555 | C22 | 1 | 2 | yes | — |
| 40 | #2956 | — | 3 | 1 | no | — |
| 41 | #2922 | — | 3 | 1 | no | — |
| 42 | #2103 | D3 | 1 | 1 | yes | characteristic, complemented |
| 43 | #2098 | — | 3 | 1 | no | — |
| 44 | #2053 | — | 3 | 1 | no | — |
| 45 | #2017 | — | 3 | 1 | no | — |
| 46 | #1937 | — | 3 | 2 | no | — |
| 47 | #1906 | — | 3 | 2 | no | — |
| 48 | #1881 | — | 3 | 2 | no | — |
| 49 | #1868 | — | 3 | 2 | no | — |
| 50 | #1841 | — | 3 | 1 | no | — |
| 51 | C2×#235 | C23 | 1 | 2 | yes | — |
| 52 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 53 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 54 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 55 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 57 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 58 | #926 | C23 | 1 | 2 | yes | — |
| 59 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 61 | C22×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 62 | #909 | — | 2 | 2 | no | — |
| 63 | #909 | — | 2 | 2 | no | — |
| 64 | #909 | — | 2 | 2 | no | — |
| 65 | #908 | — | 2 | 2 | no | — |
| 66 | #908 | — | 2 | 2 | no | — |
| 67 | #908 | — | 2 | 2 | no | — |
| 68 | #907 | — | 2 | 4 | no | — |
| 69 | D3×M16 | — | 4 | 2 | no | — |
| 70 | #904 | — | 2 | 2 | no | — |
| 71 | #904 | — | 4 | 2 | no | — |
| 72 | #901 | — | 4 | 2 | no | — |
| 73 | #893 | — | 2 | 1 | no | — |
| 74 | #887 | — | 2 | 1 | no | — |
| 75 | #67⋊C4 | — | 2 | 2 | no | — |
| 76 | #872 | — | 2 | 1 | no | — |
| 77 | C42×D3 | — | 2 | 1 | no | — |
| 78 | C3×#108 | — | 2 | 2 | no | — |
| 79 | C3×C4⋊C8 | — | 2 | 2 | no | — |
| 80 | #825 | — | 2 | 2 | no | — |
| 81 | #825 | — | 2 | 2 | no | — |
| 82 | #825 | — | 4 | 2 | no | — |
| 83 | #821 | — | 2 | 2 | no | — |
| 84 | (C2×D3)⋊C8 | — | 2 | 2 | no | — |
| 85 | (C2×D3)⋊C8 | — | 2 | 2 | no | — |
| 86 | (C2×D3)⋊C8 | — | 4 | 2 | no | — |
| 87 | #816 | — | 2 | 2 | no | — |
| 88 | #815 | D4 | 1 | 2 | yes | — |
| 89 | Dic3⋊C8 | — | 4 | 2 | no | — |
| 90 | C8×Dic3 | — | 2 | 1 | no | — |
| 91 | C8×Dic3 | — | 2 | 1 | no | — |
| 92 | C8×Dic3 | D4 | 1 | 2 | yes | — |
| 93 | #806 | — | 2 | 4 | no | — |
| 94 | C4⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 95 | #575 | — | 3 | 1 | no | — |
| 96 | #575 | — | 3 | 2 | no | — |
| 97 | #568 | — | 3 | 2 | no | — |
| 98 | C4×#41 | — | 3 | 1 | no | — |
| 99 | #444 | — | 6 | 2 | no | — |
| 100 | #443 | — | 6 | 2 | no | — |
| 101 | #433 | — | 6 | 2 | no | — |
| 102 | #431 | — | 6 | 2 | no | — |
| 103 | #430 | C2×D3 | 1 | 1 | yes | characteristic |
| 104 | #424 | — | 3 | 1 | no | — |
| 105 | #424 | — | 3 | 2 | no | — |
| 106 | #424 | C2×D3 | 1 | 1 | yes | characteristic |
| 107 | #421 | — | 3 | 2 | no | — |
| 108 | C2×#104 | — | 3 | 2 | no | — |
| 109 | #416 | — | 3 | 2 | no | — |
| 110 | #410 | — | 3 | 2 | no | — |
| 111 | #408 | — | 3 | 1 | no | — |
| 112 | #408 | — | 3 | 1 | no | — |
| 113 | #408 | — | 3 | 2 | no | — |
| 114 | C4×M16 | — | 3 | 1 | no | — |
| 115 | C2×C4×C8 | — | 3 | 1 | no | — |
| 116 | #344 | — | 3 | 2 | no | — |
| 117 | #344 | C2×D3 | 1 | 2 | yes | — |
| 118 | #341 | C2×D3 | 1 | 2 | yes | — |
| 119 | #339 | — | 3 | 2 | no | — |
| 120 | #338 | C2×D3 | 1 | 1 | yes | characteristic |
| 121 | H(3,ℤ/4) | — | 3 | 1 | no | — |
| 122 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 123 | C2×#67 | — | 2 | 2 | no | — |
| 124 | C2×#67 | — | 2 | 1 | no | — |
| 125 | C22×Dic3 | — | 2 | 1 | no | — |
| 126 | #235 | — | 2 | 2 | no | — |
| 127 | #235 | — | 2 | 2 | no | — |
| 128 | #235 | — | 2 | 2 | no | — |
| 129 | #235 | — | 2 | 2 | no | — |
| 130 | #235 | — | 2 | 2 | no | — |
| 131 | #235 | — | 2 | 2 | no | — |
| 132 | C2×D12 | #41 | 1 | 2 | yes | — |
| 133 | C2×D12 | #41 | 1 | 1 | yes | characteristic |
| 134 | C2×C4×D3 | — | 2 | 2 | no | — |
| 135 | C2×C4×D3 | — | 2 | 1 | no | — |
| 136 | C2×C4×D3 | — | 2 | 2 | no | — |
| 137 | C2×Dic6 | #41 | 1 | 2 | yes | — |
| 138 | C2×Dic6 | #41 | 1 | 1 | yes | characteristic |
| 139 | C3×M16 | — | 2 | 2 | no | — |
| 140 | C3×M16 | — | 2 | 2 | no | — |
| 141 | C3×M16 | — | 2 | 2 | no | — |
| 142 | C3×M16 | — | 2 | 2 | no | — |
| 143 | C3×M16 | — | 2 | 2 | no | — |
| 144 | C2×C3×C8 | — | 2 | 1 | no | — |
| 145 | C2×C3×C8 | — | 2 | 2 | no | — |
| 146 | C2×C3×C8 | — | 2 | 2 | no | — |
| 147 | C2×C3×C8 | — | 2 | 2 | no | — |
| 148 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 149 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 150 | C3×C22⋊C4 | #41 | 1 | 2 | yes | — |
| 151 | C3×C42 | — | 2 | 1 | no | — |
| 152 | #217 | — | 2 | 2 | no | — |
| 153 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 154 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 155 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 156 | C4×Dic3 | — | 2 | 2 | no | — |
| 157 | C4×Dic3 | — | 2 | 1 | no | — |
| 158 | C4×Dic3 | — | 2 | 2 | no | — |
| 159 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | #208 | — | 2 | 2 | no | — |
| 162 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 163 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 164 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 165 | Dic12 | — | 2 | 2 | no | — |
| 166 | Dic12 | — | 4 | 2 | no | — |
| 167 | D24 | — | 2 | 2 | no | — |
| 168 | D24 | — | 4 | 2 | no | — |
| 169 | #204 | — | 2 | 4 | no | — |
| 170 | #204 | — | 4 | 2 | no | — |
| 171 | #204 | — | 4 | 2 | no | — |
| 172 | ΓL(1,𝔽25) | — | 4 | 4 | no | — |
| 173 | D3×C8 | — | 4 | 4 | no | — |
| 174 | C2×#41 | — | 3 | 1 | no | — |
| 175 | C2×#41 | — | 3 | 2 | no | — |
| 176 | #137 | — | 6 | 2 | no | — |
| 177 | #137 | — | 6 | 2 | no | — |
| 178 | #137 | — | 6 | 2 | no | — |
| 179 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 180 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 181 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 182 | #135 | — | 6 | 2 | no | — |
| 183 | #135 | — | 12 | 2 | no | — |
| 184 | #131 | — | 6 | 4 | no | — |
| 185 | #131 | — | 12 | 2 | no | — |
| 186 | C2×M16 | — | 3 | 1 | no | — |
| 187 | C2×M16 | — | 12 | 2 | no | — |
| 188 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 189 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 190 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 191 | C22×C8 | — | 3 | 1 | no | — |
| 192 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 193 | C4×Q8 | — | 6 | 1 | no | — |
| 194 | C4×D4 | — | 6 | 1 | no | — |
| 195 | C4×D4 | — | 6 | 2 | no | — |
| 196 | #117 | — | 3 | 2 | no | — |
| 197 | #117 | — | 6 | 1 | no | — |
| 198 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 199 | C2×C42 | — | 3 | 1 | no | — |
| 200 | C2×C42 | — | 6 | 1 | no | — |
| 201 | #108 | — | 2 | 2 | no | — |
| 202 | C4⋊C8 | — | 2 | 2 | no | — |
| 203 | C4⋊C8 | — | 6 | 2 | no | — |
| 204 | C4⋊C8 | — | 12 | 2 | no | — |
| 205 | #104 | — | 6 | 2 | no | — |
| 206 | #104 | — | 6 | 2 | no | — |
| 207 | #104 | — | 12 | 2 | no | — |
| 208 | #103 | — | 6 | 2 | no | — |
| 209 | #102 | — | 6 | 2 | no | — |
| 210 | #99 | — | 6 | 4 | no | — |
| 211 | C22⋊C8 | — | 6 | 2 | no | — |
| 212 | C22⋊C8 | — | 6 | 2 | no | — |
| 213 | C22⋊C8 | — | 12 | 2 | no | — |
| 214 | #97 | — | 3 | 2 | no | — |
| 215 | C4×C8 | — | 3 | 2 | no | — |
| 216 | C4×C8 | — | 6 | 1 | no | — |
| 217 | C4×C8 | — | 6 | 1 | no | — |
| 218 | C23×C3 | C2×#41 | 1 | 1 | yes | characteristic |
| 219 | C22×D3 | — | 2 | 1 | no | — |
| 220 | C22×D3 | — | 2 | 2 | no | — |
| 221 | C2×C3×C4 | — | 2 | 2 | no | — |
| 222 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 223 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 224 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 225 | C2×C3×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 226 | #67 | — | 4 | 2 | no | — |
| 227 | #67 | — | 4 | 2 | no | — |
| 228 | #67 | — | 4 | 2 | no | — |
| 229 | C2×Dic3 | — | 2 | 1 | no | — |
| 230 | C2×Dic3 | — | 2 | 1 | no | — |
| 231 | C2×Dic3 | — | 2 | 1 | no | — |
| 232 | C2×Dic3 | — | 2 | 2 | no | — |
| 233 | C2×Dic3 | — | 4 | 2 | no | — |
| 234 | C2×Dic3 | — | 4 | 2 | no | — |
| 235 | D12 | — | 2 | 2 | no | — |
| 236 | D12 | — | 2 | 2 | no | — |
| 237 | D12 | — | 2 | 2 | no | — |
| 238 | C4×D3 | — | 4 | 4 | no | — |
| 239 | C4×D3 | — | 4 | 1 | no | — |
| 240 | C4×D3 | — | 4 | 2 | no | — |
| 241 | C4×D3 | — | 4 | 1 | no | — |
| 242 | C4×D3 | — | 4 | 2 | no | — |
| 243 | Dic6 | — | 2 | 2 | no | — |
| 244 | Dic6 | — | 2 | 2 | no | — |
| 245 | Dic6 | — | 2 | 2 | no | — |
| 246 | C3×C8 | — | 2 | 2 | no | — |
| 247 | C3×C8 | — | 4 | 1 | no | — |
| 248 | C3×C8 | — | 4 | 2 | no | — |
| 249 | C3×C8 | — | 4 | 2 | no | — |
| 250 | C3⋊C8 | — | 2 | 2 | no | — |
| 251 | C3⋊C8 | — | 4 | 1 | no | — |
| 252 | #41 | — | 6 | 2 | no | — |
| 253 | #41 | — | 6 | 2 | no | — |
| 254 | #41 | — | 6 | 2 | no | — |
| 255 | #41 | — | 6 | 2 | no | — |
| 256 | #41 | — | 6 | 2 | no | — |
| 257 | #41 | — | 6 | 2 | no | — |
| 258 | C2×Q8 | — | 3 | 2 | no | — |
| 259 | C2×Q8 | — | 3 | 1 | no | — |
| 260 | C2×D4 | — | 3 | 2 | no | — |
| 261 | C2×D4 | — | 3 | 1 | no | — |
| 262 | C2×D4 | — | 6 | 2 | no | — |
| 263 | C2×D4 | — | 6 | 1 | no | — |
| 264 | C22×C4 | — | 6 | 2 | no | — |
| 265 | C22×C4 | — | 6 | 1 | no | — |
| 266 | C22×C4 | — | 6 | 1 | no | — |
| 267 | C22×C4 | — | 6 | 2 | no | — |
| 268 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 269 | Q16 | — | 6 | 2 | no | — |
| 270 | Q16 | — | 12 | 2 | no | — |
| 271 | SD16 | — | 6 | 4 | no | — |
| 272 | SD16 | — | 12 | 2 | no | — |
| 273 | SD16 | — | 12 | 2 | no | — |
| 274 | D8 | — | 6 | 2 | no | — |
| 275 | D8 | — | 12 | 2 | no | — |
| 276 | M16 | — | 2 | 2 | no | — |
| 277 | M16 | — | 2 | 2 | no | — |
| 278 | M16 | — | 2 | 2 | no | — |
| 279 | M16 | — | 2 | 2 | no | — |
| 280 | M16 | — | 2 | 2 | no | — |
| 281 | M16 | — | 6 | 2 | no | — |
| 282 | M16 | — | 12 | 4 | no | — |
| 283 | C2×C8 | — | 2 | 1 | no | — |
| 284 | C2×C8 | — | 2 | 2 | no | — |
| 285 | C2×C8 | — | 2 | 2 | no | — |
| 286 | C2×C8 | — | 2 | 2 | no | — |
| 287 | C2×C8 | — | 3 | 2 | no | — |
| 288 | C2×C8 | — | 6 | 1 | no | — |
| 289 | C2×C8 | — | 6 | 2 | no | — |
| 290 | C2×C8 | — | 12 | 4 | no | — |
| 291 | C2×C8 | D3×D4 | 1 | 2 | yes | — |
| 292 | C4⋊C4 | — | 2 | 1 | no | — |
| 293 | C4⋊C4 | — | 6 | 2 | no | — |
| 294 | C4⋊C4 | — | 6 | 2 | no | — |
| 295 | C22⋊C4 | — | 6 | 2 | no | — |
| 296 | C22⋊C4 | — | 6 | 2 | no | — |
| 297 | C22⋊C4 | #239 | 1 | 2 | yes | — |
| 298 | C42 | — | 2 | 1 | no | — |
| 299 | C42 | — | 3 | 1 | no | — |
| 300 | C42 | — | 3 | 1 | no | — |
| 301 | C42 | — | 6 | 2 | no | — |
| 302 | C42 | — | 6 | 1 | no | — |
| 303 | C42 | — | 6 | 2 | no | — |
| 304 | C22×C3 | — | 4 | 1 | no | — |
| 305 | C22×C3 | #525 | 1 | 1 | yes | characteristic |
| 306 | C22×C3 | #553 | 1 | 2 | yes | — |
| 307 | C2×D3 | — | 4 | 2 | no | — |
| 308 | C2×D3 | — | 4 | 1 | no | — |
| 309 | C2×D3 | — | 4 | 2 | no | — |
| 310 | C2×D3 | — | 8 | 2 | no | — |
| 311 | C3×C4 | — | 4 | 2 | no | — |
| 312 | C3×C4 | #525 | 1 | 1 | yes | characteristic |
| 313 | C3×C4 | #535 | 1 | 1 | yes | characteristic |
| 314 | C3×C4 | #551 | 1 | 2 | yes | — |
| 315 | Dic3 | — | 2 | 2 | no | — |
| 316 | Dic3 | — | 4 | 1 | no | — |
| 317 | Dic3 | — | 4 | 2 | no | — |
| 318 | Dic3 | — | 4 | 1 | no | — |
| 319 | Dic3 | — | 8 | 2 | no | — |
| 320 | C23 | — | 6 | 1 | no | — |
| 321 | C23 | — | 6 | 2 | no | — |
| 322 | C23 | C2×#239 | 1 | 1 | yes | characteristic |
| 323 | Q8 | — | 6 | 2 | no | — |
| 324 | Q8 | — | 6 | 2 | no | — |
| 325 | Q8 | — | 6 | 2 | no | — |
| 326 | D4 | — | 6 | 2 | no | — |
| 327 | D4 | — | 6 | 2 | no | — |
| 328 | D4 | — | 6 | 2 | no | — |
| 329 | D4 | — | 12 | 2 | no | — |
| 330 | D4 | — | 12 | 2 | no | — |
| 331 | D4 | — | 12 | 2 | no | — |
| 332 | C2×C4 | — | 2 | 2 | no | — |
| 333 | C2×C4 | — | 6 | 1 | no | — |
| 334 | C2×C4 | — | 6 | 2 | no | — |
| 335 | C2×C4 | — | 6 | 1 | no | — |
| 336 | C2×C4 | — | 6 | 1 | no | — |
| 337 | C2×C4 | — | 12 | 4 | no | — |
| 338 | C2×C4 | — | 12 | 2 | no | — |
| 339 | C2×C4 | — | 12 | 1 | no | — |
| 340 | C2×C4 | — | 12 | 2 | no | — |
| 341 | C2×C4 | — | 12 | 1 | no | — |
| 342 | C2×C4 | — | 12 | 2 | no | — |
| 343 | C2×C4 | — | 12 | 2 | no | — |
| 344 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 345 | C2×C4 | D3×#41 | 1 | 2 | yes | — |
| 346 | C2×C4 | D3×#41 | 1 | 1 | yes | characteristic |
| 347 | C2×C4 | #1009 | 1 | 2 | yes | — |
| 348 | C8 | — | 2 | 2 | no | — |
| 349 | C8 | — | 4 | 1 | no | — |
| 350 | C8 | — | 4 | 2 | no | — |
| 351 | C8 | — | 4 | 2 | no | — |
| 352 | C8 | — | 6 | 2 | no | — |
| 353 | C8 | — | 12 | 1 | no | — |
| 354 | C2×C3 | — | 2 | 1 | no | — |
| 355 | C2×C3 | — | 2 | 2 | no | — |
| 356 | C2×C3 | #2598 | 1 | 1 | yes | characteristic |
| 357 | D3 | — | 8 | 1 | no | — |
| 358 | D3 | — | 8 | 2 | no | — |
| 359 | C22 | — | 4 | 1 | no | — |
| 360 | C22 | — | 12 | 2 | no | — |
| 361 | C22 | — | 12 | 1 | no | — |
| 362 | C22 | — | 12 | 2 | no | — |
| 363 | C22 | — | 24 | 2 | no | — |
| 364 | C22 | #5627 | 1 | 1 | yes | characteristic |
| 365 | C22 | #5695 | 1 | 2 | yes | — |
| 366 | C4 | — | 4 | 2 | no | — |
| 367 | C4 | — | 6 | 2 | no | — |
| 368 | C4 | — | 12 | 1 | no | — |
| 369 | C4 | — | 12 | 2 | no | — |
| 370 | C4 | — | 12 | 1 | no | — |
| 371 | C4 | — | 24 | 2 | no | — |
| 372 | C4 | #5656 | 1 | 1 | yes | characteristic |
| 373 | C4 | #5674 | 1 | 1 | yes | characteristic |
| 374 | C4 | #5705 | 1 | 2 | yes | — |
| 375 | C3 | #29386 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 376 | C2 | — | 2 | 1 | no | — |
| 377 | C2 | — | 2 | 2 | no | — |
| 378 | C2 | — | 24 | 1 | no | — |
| 379 | C2 | — | 24 | 2 | no | — |
| 380 | C2 | #78203 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #79258 | C2 | semidirect |
| 2. #79070 | C2 | semidirect |
| 3. C3×#2103 | C2 | semidirect |
| 4. #70738 | C2 | semidirect |
| 5. #70547 | C2 | semidirect |
| 6. #69039 | C2 | semidirect |
| 7. #69034 | C2 | semidirect |
| 8. #68947 | C2 | semidirect |
| 9. #68918 | C2 | semidirect |
| 11. #68716 | C2 | semidirect |
| 42. #2103 | D3 | semidirect |
| 375. C3 | #29386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79258 | 2 |
| #79070 | 2 |
| C3×#2103 | 2 |
| #70738 | 2 |
| #70547 | 2 |
| #69039 | 2 |
| #69034 | 2 |
| #68947 | 2 |
| #68918 | 2 |
| #68727 | 2 |
| #68716 | 2 |
| #29386 | 3 |