Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
642 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 113 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 | #79303 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #78538 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#4694 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #70778 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #69876 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #69735 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#1278 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10168 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C2×#909 | — | 2 | 2 | no | — |
| 10 | #5477 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#874 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#869 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×#431 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×C4×M16 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3×C4×C8 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#823 | — | 2 | 2 | no | — |
| 17 | C2×#821 | — | 2 | 2 | no | — |
| 18 | #4924 | C22 | 1 | 1 | yes | characteristic |
| 19 | #4843 | — | 2 | 2 | no | — |
| 20 | #4732 | — | 2 | 2 | no | — |
| 21 | #4715 | — | 2 | 2 | no | — |
| 22 | #4699 | — | 2 | 1 | no | — |
| 23 | #4695 | — | 2 | 1 | no | — |
| 24 | #4694 | — | 2 | 2 | no | — |
| 25 | #4694 | — | 2 | 1 | no | — |
| 26 | #4694 | — | 2 | 2 | no | — |
| 27 | #4693 | — | 2 | 1 | no | — |
| 28 | #4486 | — | 2 | 2 | no | — |
| 29 | #4459 | — | 2 | 2 | no | — |
| 30 | #3205 | — | 3 | 1 | no | — |
| 31 | #3152 | — | 3 | 1 | no | — |
| 32 | C2×#486 | — | 3 | 1 | no | — |
| 33 | #1965 | — | 3 | 1 | no | — |
| 34 | #1546 | — | 3 | 1 | no | — |
| 35 | #1492 | — | 3 | 1 | no | — |
| 36 | #1278 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C2×#235 | — | 2 | 1 | no | — |
| 38 | C22×D12 | — | 2 | 1 | no | — |
| 39 | C22×D12 | — | 2 | 1 | no | — |
| 40 | C22×D12 | D4 | 1 | 2 | yes | — |
| 41 | C22×Dic6 | — | 2 | 1 | no | — |
| 42 | C2×C3×M16 | D4 | 1 | 2 | yes | — |
| 43 | C22×C3×C8 | — | 2 | 1 | no | — |
| 44 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 45 | #930 | — | 2 | 1 | no | — |
| 46 | #930 | — | 2 | 1 | no | — |
| 47 | C2×C4⋊Dic3 | — | 2 | 1 | no | — |
| 48 | C2×C4⋊Dic3 | — | 2 | 1 | no | — |
| 49 | C2×#208 | — | 2 | 1 | no | — |
| 50 | #909 | — | 4 | 4 | no | — |
| 51 | #909 | — | 4 | 4 | no | — |
| 52 | C2×Dic12 | — | 2 | 4 | no | — |
| 53 | C2×D24 | — | 2 | 4 | no | — |
| 54 | C2×#204 | — | 2 | 4 | no | — |
| 55 | #875 | — | 2 | 1 | no | — |
| 56 | #874 | — | 2 | 1 | no | — |
| 57 | #874 | — | 2 | 1 | no | — |
| 58 | #874 | — | 2 | 1 | no | — |
| 59 | #874 | — | 2 | 1 | no | — |
| 60 | #874 | D4 | 1 | 1 | yes | characteristic |
| 61 | C4×D12 | — | 2 | 1 | no | — |
| 62 | C4×D12 | — | 2 | 1 | no | — |
| 63 | #869 | — | 2 | 1 | no | — |
| 64 | #869 | — | 2 | 1 | no | — |
| 65 | #869 | — | 2 | 1 | no | — |
| 66 | #869 | D4 | 1 | 1 | yes | characteristic |
| 67 | #869 | D4 | 1 | 2 | yes | — |
| 68 | C3×C4⋊C8 | D4 | 1 | 2 | yes | — |
| 69 | C3×C22⋊C8 | — | 2 | 1 | no | — |
| 70 | C3×#97 | — | 2 | 1 | no | — |
| 71 | C3×C4×C8 | — | 2 | 1 | no | — |
| 72 | C3×C4×C8 | — | 2 | 1 | no | — |
| 73 | C3×C4×C8 | — | 2 | 1 | no | — |
| 74 | C3×C4×C8 | D4 | 1 | 2 | yes | — |
| 75 | #823 | — | 4 | 4 | no | — |
| 76 | #821 | — | 2 | 8 | no | — |
| 77 | #821 | — | 2 | 4 | no | — |
| 78 | C4⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 79 | C4⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 80 | C2×#137 | — | 6 | 2 | no | — |
| 81 | #532 | — | 3 | 1 | no | — |
| 82 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 83 | C2×#127 | — | 3 | 1 | no | — |
| 84 | #497 | — | 6 | 2 | no | — |
| 85 | #494 | — | 6 | 1 | no | — |
| 86 | #493 | — | 6 | 1 | no | — |
| 87 | #492 | — | 6 | 1 | no | — |
| 88 | #486 | — | 6 | 2 | no | — |
| 89 | #486 | — | 6 | 1 | no | — |
| 90 | #486 | — | 6 | 2 | no | — |
| 91 | #459 | — | 6 | 2 | no | — |
| 92 | #447 | — | 6 | 2 | no | — |
| 93 | #431 | C2×D3 | 1 | 1 | yes | characteristic |
| 94 | #423 | — | 3 | 1 | no | — |
| 95 | C2×#102 | — | 6 | 2 | no | — |
| 96 | C2×#100 | — | 6 | 2 | no | — |
| 97 | C4×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 98 | C2×C4×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 99 | #332 | — | 6 | 2 | no | — |
| 100 | D4⋊C8 | — | 6 | 2 | no | — |
| 101 | C23×D3 | — | 2 | 2 | no | — |
| 102 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C22×C3×C4 | #41 | 1 | 1 | yes | characteristic |
| 105 | C2×#67 | — | 4 | 1 | no | — |
| 106 | C22×Dic3 | — | 4 | 1 | no | — |
| 107 | #235 | — | 4 | 2 | no | — |
| 108 | #235 | — | 4 | 2 | no | — |
| 109 | C2×D12 | — | 2 | 2 | no | — |
| 110 | C2×D12 | — | 2 | 2 | no | — |
| 111 | C2×D12 | — | 2 | 1 | no | — |
| 112 | C2×D12 | — | 2 | 1 | no | — |
| 113 | C2×D12 | — | 2 | 1 | no | — |
| 114 | C2×D12 | — | 4 | 4 | no | — |
| 115 | C2×D12 | — | 4 | 1 | no | — |
| 116 | C2×D12 | — | 4 | 1 | no | — |
| 117 | C2×D12 | — | 4 | 1 | no | — |
| 118 | C2×D12 | — | 4 | 1 | no | — |
| 119 | C2×D12 | — | 4 | 2 | no | — |
| 120 | C2×D12 | — | 4 | 2 | no | — |
| 121 | C2×D12 | — | 8 | 2 | no | — |
| 122 | C2×C4×D3 | — | 4 | 1 | no | — |
| 123 | C2×Dic6 | — | 2 | 2 | no | — |
| 124 | C2×Dic6 | — | 2 | 1 | no | — |
| 125 | C2×Dic6 | — | 4 | 2 | no | — |
| 126 | C2×Dic6 | — | 4 | 2 | no | — |
| 127 | C2×Dic6 | — | 4 | 1 | no | — |
| 128 | C3×M16 | — | 2 | 2 | no | — |
| 129 | C3×M16 | D8 | 1 | 4 | yes | complemented |
| 130 | C2×C3×C8 | — | 2 | 2 | no | — |
| 131 | C2×C3×C8 | — | 2 | 2 | no | — |
| 132 | C2×C3×C8 | — | 2 | 2 | no | — |
| 133 | C2×C3×C8 | — | 4 | 2 | no | — |
| 134 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 139 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 140 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 141 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 142 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 143 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 144 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 145 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 146 | #208 | — | 4 | 2 | no | — |
| 147 | C2×C3⋊C8 | — | 4 | 1 | no | — |
| 148 | Dic12 | — | 4 | 8 | no | — |
| 149 | D24 | — | 8 | 4 | no | — |
| 150 | #204 | — | 4 | 8 | no | — |
| 151 | C2×#41 | — | 6 | 1 | no | — |
| 152 | C22×Q8 | — | 6 | 1 | no | — |
| 153 | C22×D4 | — | 3 | 2 | no | — |
| 154 | C22×D4 | — | 6 | 1 | no | — |
| 155 | C22×D4 | — | 6 | 1 | no | — |
| 156 | #137 | — | 12 | 4 | no | — |
| 157 | #137 | — | 12 | 4 | no | — |
| 158 | C2×Q16 | — | 6 | 4 | no | — |
| 159 | C2×SD16 | — | 6 | 4 | no | — |
| 160 | C2×D8 | — | 6 | 4 | no | — |
| 161 | C2×M16 | — | 6 | 1 | no | — |
| 162 | C2×M16 | D12 | 1 | 2 | yes | — |
| 163 | C22×C8 | — | 2 | 1 | no | — |
| 164 | C4⋊Q8 | — | 3 | 2 | no | — |
| 165 | C4⋊Q8 | — | 3 | 1 | no | — |
| 166 | C4⋊Q8 | — | 6 | 1 | no | — |
| 167 | C4⋊Q8 | — | 6 | 1 | no | — |
| 168 | C4⋊Q8 | — | 6 | 1 | no | — |
| 169 | #127 | — | 3 | 1 | no | — |
| 170 | #127 | — | 6 | 1 | no | — |
| 171 | #127 | — | 6 | 1 | no | — |
| 172 | #127 | — | 6 | 1 | no | — |
| 173 | #127 | — | 6 | 1 | no | — |
| 174 | #124 | — | 6 | 1 | no | — |
| 175 | #121 | — | 6 | 1 | no | — |
| 176 | #121 | — | 6 | 1 | no | — |
| 177 | C4×D4 | — | 6 | 1 | no | — |
| 178 | C4×D4 | — | 6 | 1 | no | — |
| 179 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 180 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 181 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 182 | C4⋊C8 | — | 6 | 1 | no | — |
| 183 | C4⋊C8 | — | 6 | 1 | no | — |
| 184 | C4⋊C8 | D12 | 1 | 2 | yes | — |
| 185 | #102 | — | 6 | 8 | no | — |
| 186 | #102 | — | 6 | 4 | no | — |
| 187 | #100 | — | 12 | 4 | no | — |
| 188 | C22⋊C8 | — | 2 | 1 | no | — |
| 189 | #97 | — | 2 | 1 | no | — |
| 190 | C4×C8 | — | 2 | 1 | no | — |
| 191 | C4×C8 | — | 2 | 1 | no | — |
| 192 | C4×C8 | — | 2 | 1 | no | — |
| 193 | C4×C8 | D12 | 1 | 2 | yes | — |
| 194 | C23×C3 | #121 | 1 | 1 | yes | characteristic |
| 195 | C22×D3 | — | 4 | 1 | no | — |
| 196 | C22×D3 | — | 4 | 2 | no | — |
| 197 | C22×D3 | — | 4 | 4 | no | — |
| 198 | C22×D3 | — | 8 | 2 | no | — |
| 199 | C22×D3 | — | 8 | 2 | no | — |
| 200 | C2×C3×C4 | — | 2 | 2 | no | — |
| 201 | C2×C3×C4 | — | 2 | 2 | no | — |
| 202 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 203 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 204 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 205 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 206 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 207 | C2×C3×C4 | #127 | 1 | 1 | yes | characteristic |
| 208 | C2×C3×C4 | C2×D8 | 1 | 2 | yes | — |
| 209 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 210 | #67 | — | 8 | 2 | no | — |
| 211 | C2×Dic3 | — | 4 | 2 | no | — |
| 212 | C2×Dic3 | — | 4 | 1 | no | — |
| 213 | C2×Dic3 | — | 8 | 2 | no | — |
| 214 | D12 | — | 4 | 4 | no | — |
| 215 | D12 | — | 4 | 2 | no | — |
| 216 | D12 | — | 4 | 2 | no | — |
| 217 | D12 | — | 4 | 4 | no | — |
| 218 | D12 | — | 4 | 2 | no | — |
| 219 | D12 | — | 8 | 2 | no | — |
| 220 | D12 | — | 8 | 2 | no | — |
| 221 | D12 | — | 8 | 2 | no | — |
| 222 | D12 | — | 8 | 1 | no | — |
| 223 | D12 | — | 8 | 1 | no | — |
| 224 | C4×D3 | — | 8 | 1 | no | — |
| 225 | C4×D3 | — | 8 | 1 | no | — |
| 226 | Dic6 | — | 4 | 4 | no | — |
| 227 | Dic6 | — | 4 | 2 | no | — |
| 228 | Dic6 | — | 8 | 1 | no | — |
| 229 | Dic6 | — | 8 | 1 | no | — |
| 230 | C3×C8 | — | 2 | 4 | no | — |
| 231 | C3×C8 | — | 4 | 2 | no | — |
| 232 | C3×C8 | — | 4 | 2 | no | — |
| 233 | C3⋊C8 | — | 8 | 1 | no | — |
| 234 | C24 | — | 6 | 2 | no | — |
| 235 | #41 | — | 12 | 2 | no | — |
| 236 | #41 | — | 12 | 2 | no | — |
| 237 | C2×Q8 | — | 6 | 1 | no | — |
| 238 | C2×Q8 | — | 6 | 2 | no | — |
| 239 | C2×Q8 | — | 12 | 1 | no | — |
| 240 | C2×Q8 | — | 12 | 2 | no | — |
| 241 | C2×Q8 | — | 12 | 2 | no | — |
| 242 | C2×D4 | — | 6 | 2 | no | — |
| 243 | C2×D4 | — | 6 | 2 | no | — |
| 244 | C2×D4 | — | 6 | 1 | no | — |
| 245 | C2×D4 | — | 6 | 1 | no | — |
| 246 | C2×D4 | — | 6 | 1 | no | — |
| 247 | C2×D4 | — | 12 | 4 | no | — |
| 248 | C2×D4 | — | 12 | 1 | no | — |
| 249 | C2×D4 | — | 12 | 1 | no | — |
| 250 | C2×D4 | — | 12 | 1 | no | — |
| 251 | C2×D4 | — | 12 | 1 | no | — |
| 252 | C2×D4 | — | 12 | 1 | no | — |
| 253 | C2×D4 | — | 12 | 2 | no | — |
| 254 | C2×D4 | — | 12 | 2 | no | — |
| 255 | C2×D4 | — | 24 | 2 | no | — |
| 256 | C22×C4 | — | 12 | 1 | no | — |
| 257 | C22×C4 | — | 12 | 1 | no | — |
| 258 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 259 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 260 | C22×C4 | #239 | 1 | 1 | yes | characteristic |
| 261 | Q16 | — | 12 | 8 | no | — |
| 262 | SD16 | — | 12 | 8 | no | — |
| 263 | D8 | — | 24 | 4 | no | — |
| 264 | M16 | — | 2 | 2 | no | — |
| 265 | M16 | — | 12 | 2 | no | — |
| 266 | M16 | D24 | 1 | 4 | yes | complemented |
| 267 | C2×C8 | — | 2 | 2 | no | — |
| 268 | C2×C8 | — | 2 | 2 | no | — |
| 269 | C2×C8 | — | 2 | 2 | no | — |
| 270 | C2×C8 | — | 4 | 2 | no | — |
| 271 | C2×C8 | — | 12 | 1 | no | — |
| 272 | C4⋊C4 | — | 6 | 2 | no | — |
| 273 | C4⋊C4 | — | 6 | 1 | no | — |
| 274 | C4⋊C4 | — | 6 | 2 | no | — |
| 275 | C4⋊C4 | — | 6 | 1 | no | — |
| 276 | C4⋊C4 | — | 12 | 1 | no | — |
| 277 | C4⋊C4 | — | 12 | 1 | no | — |
| 278 | C22⋊C4 | — | 12 | 1 | no | — |
| 279 | C22⋊C4 | — | 12 | 1 | no | — |
| 280 | C42 | C2×D12 | 1 | 1 | yes | characteristic |
| 281 | C42 | C2×D12 | 1 | 1 | yes | characteristic |
| 282 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 283 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 284 | C22×C3 | — | 2 | 1 | no | — |
| 285 | C22×C3 | — | 2 | 1 | no | — |
| 286 | C22×C3 | #392 | 1 | 1 | yes | characteristic |
| 287 | C22×C3 | #459 | 1 | 2 | yes | — |
| 288 | C2×D3 | — | 8 | 2 | no | — |
| 289 | C2×D3 | — | 8 | 1 | no | — |
| 290 | C2×D3 | — | 8 | 1 | no | — |
| 291 | C2×D3 | — | 8 | 2 | no | — |
| 292 | C2×D3 | — | 8 | 1 | no | — |
| 293 | C2×D3 | — | 8 | 2 | no | — |
| 294 | C2×D3 | — | 16 | 4 | no | — |
| 295 | C3×C4 | — | 2 | 1 | no | — |
| 296 | C3×C4 | — | 2 | 1 | no | — |
| 297 | C3×C4 | #447 | 1 | 2 | yes | — |
| 298 | C3×C4 | #455 | 1 | 2 | yes | — |
| 299 | C3×C4 | #471 | 1 | 2 | yes | — |
| 300 | C3×C4 | #493 | 1 | 1 | yes | characteristic |
| 301 | C3×C4 | #496 | 1 | 1 | yes | characteristic |
| 302 | Dic3 | — | 8 | 2 | no | — |
| 303 | Dic3 | — | 8 | 1 | no | — |
| 304 | C23 | — | 12 | 1 | no | — |
| 305 | C23 | — | 12 | 2 | no | — |
| 306 | C23 | — | 12 | 4 | no | — |
| 307 | C23 | — | 24 | 2 | no | — |
| 308 | C23 | — | 24 | 2 | no | — |
| 309 | C23 | #895 | 1 | 1 | yes | characteristic |
| 310 | Q8 | — | 12 | 4 | no | — |
| 311 | Q8 | — | 12 | 2 | no | — |
| 312 | Q8 | — | 24 | 1 | no | — |
| 313 | Q8 | — | 24 | 1 | no | — |
| 314 | D4 | — | 12 | 4 | no | — |
| 315 | D4 | — | 12 | 2 | no | — |
| 316 | D4 | — | 12 | 2 | no | — |
| 317 | D4 | — | 12 | 2 | no | — |
| 318 | D4 | — | 12 | 4 | no | — |
| 319 | D4 | — | 24 | 2 | no | — |
| 320 | D4 | — | 24 | 2 | no | — |
| 321 | D4 | — | 24 | 2 | no | — |
| 322 | D4 | — | 24 | 1 | no | — |
| 323 | D4 | — | 24 | 1 | no | — |
| 324 | D4 | — | 24 | 2 | no | — |
| 325 | C2×C4 | — | 2 | 2 | no | — |
| 326 | C2×C4 | — | 2 | 2 | no | — |
| 327 | C2×C4 | — | 12 | 1 | no | — |
| 328 | C2×C4 | — | 12 | 2 | no | — |
| 329 | C2×C4 | — | 24 | 2 | no | — |
| 330 | C2×C4 | — | 24 | 1 | no | — |
| 331 | C2×C4 | — | 24 | 1 | no | — |
| 332 | C2×C4 | #874 | 1 | 1 | yes | characteristic |
| 333 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 334 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 335 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 336 | C2×C4 | #895 | 1 | 1 | yes | characteristic |
| 337 | C2×C4 | #895 | 1 | 1 | yes | characteristic |
| 338 | C2×C4 | C2×D24 | 1 | 2 | yes | — |
| 339 | C2×C4 | #908 | 1 | 2 | yes | — |
| 340 | C8 | — | 2 | 4 | no | — |
| 341 | C8 | — | 4 | 2 | no | — |
| 342 | C8 | — | 4 | 2 | no | — |
| 343 | C8 | — | 24 | 1 | no | — |
| 344 | C2×C3 | — | 2 | 2 | no | — |
| 345 | C2×C3 | #2004 | 1 | 1 | yes | characteristic |
| 346 | C2×C3 | #2011 | 1 | 1 | yes | characteristic |
| 347 | C2×C3 | #2019 | 1 | 1 | yes | characteristic |
| 348 | D3 | — | 16 | 1 | no | — |
| 349 | D3 | — | 16 | 2 | no | — |
| 350 | C22 | — | 2 | 1 | no | — |
| 351 | C22 | — | 2 | 1 | no | — |
| 352 | C22 | — | 24 | 1 | no | — |
| 353 | C22 | — | 24 | 2 | no | — |
| 354 | C22 | — | 24 | 1 | no | — |
| 355 | C22 | — | 24 | 2 | no | — |
| 356 | C22 | — | 24 | 2 | no | — |
| 357 | C22 | — | 24 | 1 | no | — |
| 358 | C22 | — | 48 | 4 | no | — |
| 359 | C22 | #4671 | 1 | 1 | yes | characteristic |
| 360 | C22 | #4843 | 1 | 2 | yes | — |
| 361 | C4 | — | 2 | 1 | no | — |
| 362 | C4 | — | 2 | 1 | no | — |
| 363 | C4 | — | 24 | 1 | no | — |
| 364 | C4 | — | 24 | 2 | no | — |
| 365 | C4 | #4695 | 1 | 1 | yes | characteristic |
| 366 | C4 | #4712 | 1 | 1 | yes | characteristic |
| 367 | C4 | #4732 | 1 | 2 | yes | — |
| 368 | C4 | #4825 | 1 | 2 | yes | — |
| 369 | C4 | #4898 | 1 | 2 | yes | — |
| 370 | C3 | #10168 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 371 | C2 | — | 2 | 2 | no | — |
| 372 | C2 | — | 48 | 2 | no | — |
| 373 | C2 | — | 48 | 1 | no | — |
| 374 | C2 | #68674 | 1 | 1 | yes | characteristic |
| 375 | C2 | #68762 | 1 | 1 | yes | characteristic |
| 376 | C2 | #68943 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #78538 | C2 | semidirect |
| 3. C2×#4694 | C2 | semidirect |
| 4. #70778 | C2 | semidirect |
| 5. #69876 | C2 | semidirect |
| 6. #69735 | C2 | semidirect |
| 7. C3×#1278 | C2 | semidirect |
| 36. #1278 | D3 | semidirect |
| 129. C3×M16 | D8 | semidirect |
| 266. M16 | D24 | semidirect |
| 370. C3 | #10168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79303 | 2 |
| #78538 | 2 |
| C2×#4694 | 2 |
| #70778 | 2 |
| #69876 | 2 |
| #69735 | 2 |
| C3×#1278 | 2 |
| #10168 | 3 |