Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
392 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 53 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 | #22599232 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22590293 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22590290 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22589445 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #22586333 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22586277 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C71×#1342 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #17986799 | — | 2 | 1 | no | — |
| 9 | #17986799 | C22 | 1 | 1 | yes | characteristic |
| 10 | #17986572 | — | 2 | 1 | no | — |
| 11 | #17986442 | — | 2 | 1 | no | — |
| 12 | #17986440 | — | 2 | 1 | no | — |
| 13 | #17986343 | — | 2 | 1 | no | — |
| 14 | #17986338 | — | 2 | 1 | no | — |
| 15 | #17986257 | C22 | 1 | 1 | yes | characteristic |
| 16 | #17986238 | — | 2 | 1 | no | — |
| 17 | #17986156 | — | 2 | 1 | no | — |
| 18 | #17986153 | — | 2 | 1 | no | — |
| 19 | #17985967 | — | 2 | 1 | no | — |
| 20 | #17985967 | C22 | 1 | 1 | yes | characteristic |
| 21 | #17985810 | — | 2 | 1 | no | — |
| 22 | #17985808 | — | 2 | 1 | no | — |
| 23 | #17985781 | C22 | 1 | 1 | yes | characteristic |
| 24 | #470×C71 | C22 | 1 | 1 | yes | characteristic |
| 25 | #349×C71 | C22 | 1 | 1 | yes | characteristic |
| 26 | #338×C71 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#11765865 | — | 2 | 1 | no | — |
| 28 | C2×#11765865 | D4 | 1 | 1 | yes | characteristic |
| 29 | C2×Q8×D71 | — | 2 | 1 | no | — |
| 30 | #14556161 | — | 4 | 1 | no | — |
| 31 | #14556161 | — | 4 | 1 | no | — |
| 32 | #14556161 | — | 4 | 1 | no | — |
| 33 | #14556156 | — | 4 | 1 | no | — |
| 34 | #14556156 | — | 4 | 1 | no | — |
| 35 | #14556156 | — | 4 | 1 | no | — |
| 36 | #14556150 | — | 2 | 1 | no | — |
| 37 | #14556150 | — | 2 | 1 | no | — |
| 38 | #14556150 | — | 4 | 2 | no | — |
| 39 | C2×Dic284 | D4 | 1 | 1 | yes | characteristic |
| 40 | C2×#11765855 | — | 2 | 1 | no | — |
| 41 | C22×C71⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 42 | #14556127 | — | 4 | 1 | no | — |
| 43 | #14556114 | — | 4 | 1 | no | — |
| 44 | #14556113 | — | 4 | 1 | no | — |
| 45 | #14556110 | — | 4 | 1 | no | — |
| 46 | #14556108 | — | 2 | 1 | no | — |
| 47 | #14556107 | — | 2 | 1 | no | — |
| 48 | #14556104 | — | 2 | 1 | no | — |
| 49 | #14556086 | — | 2 | 1 | no | — |
| 50 | Dic568 | — | 4 | 1 | no | — |
| 51 | #14556074 | — | 4 | 1 | no | — |
| 52 | #14556073 | — | 4 | 1 | no | — |
| 53 | #14556071 | — | 4 | 1 | no | — |
| 54 | #14556068 | — | 2 | 1 | no | — |
| 55 | #14556061 | — | 2 | 1 | no | — |
| 56 | #14556060 | D4 | 1 | 1 | yes | characteristic |
| 57 | #14556053 | — | 2 | 1 | no | — |
| 58 | #14556052 | — | 2 | 1 | no | — |
| 59 | #14556051 | — | 2 | 1 | no | — |
| 60 | (C2×D71)⋊C8 | — | 2 | 1 | no | — |
| 61 | (C2×D71)⋊C8 | — | 2 | 1 | no | — |
| 62 | (C2×D71)⋊C8 | — | 4 | 2 | no | — |
| 63 | C2×Q16×C71 | D4 | 1 | 1 | yes | characteristic |
| 64 | C2×M16×C71 | — | 2 | 1 | no | — |
| 65 | C2×M16×C71 | C23 | 1 | 1 | yes | characteristic |
| 66 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 67 | M32×C71 | — | 2 | 1 | no | — |
| 68 | #106×C71 | D4 | 1 | 1 | yes | characteristic |
| 69 | #103×C71 | — | 2 | 1 | no | — |
| 70 | #11765865 | — | 4 | 1 | no | — |
| 71 | #11765865 | — | 4 | 1 | no | — |
| 72 | #11765865 | — | 4 | 1 | no | — |
| 73 | #11765865 | — | 4 | 1 | no | — |
| 74 | #11765865 | — | 4 | 1 | no | — |
| 75 | #11765865 | — | 4 | 1 | no | — |
| 76 | C2×Dic142 | — | 2 | 1 | no | — |
| 77 | C2×Dic142 | — | 2 | 1 | no | — |
| 78 | C2×Dic142 | — | 4 | 1 | no | — |
| 79 | C2×Dic142 | D8 | 1 | 1 | yes | characteristic |
| 80 | Q8×D71 | — | 8 | 1 | no | — |
| 81 | Q8×D71 | — | 8 | 1 | no | — |
| 82 | C2×D284 | — | 2 | 1 | no | — |
| 83 | C2×D284 | D8 | 1 | 1 | yes | characteristic |
| 84 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 85 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 86 | C2×C4×D71 | — | 2 | 1 | no | — |
| 87 | C2×C4×D71 | — | 4 | 1 | no | — |
| 88 | C2×C4×D71 | — | 4 | 1 | no | — |
| 89 | Dic284 | — | 2 | 1 | no | — |
| 90 | Dic284 | — | 2 | 1 | no | — |
| 91 | Dic284 | — | 4 | 1 | no | — |
| 92 | Dic284 | — | 4 | 2 | no | — |
| 93 | #11765855 | — | 8 | 1 | no | — |
| 94 | #11765854 | — | 4 | 1 | no | — |
| 95 | #11765854 | — | 4 | 1 | no | — |
| 96 | #11765854 | — | 4 | 2 | no | — |
| 97 | #11765854 | — | 4 | 2 | no | — |
| 98 | D568 | — | 2 | 1 | no | — |
| 99 | D568 | — | 2 | 1 | no | — |
| 100 | D568 | — | 4 | 2 | no | — |
| 101 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 102 | C2×C71⋊C8 | — | 4 | 1 | no | — |
| 103 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 104 | C4⋊Dic71 | — | 4 | 1 | no | — |
| 105 | Dic71⋊C4 | — | 4 | 1 | no | — |
| 106 | Dic71⋊C4 | — | 4 | 1 | no | — |
| 107 | C22⋊Dic71 | — | 4 | 1 | no | — |
| 108 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 109 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 110 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 111 | C4×Dic71 | — | 4 | 1 | no | — |
| 112 | C71⋊C16 | — | 4 | 1 | no | — |
| 113 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 114 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | Q16×C71 | — | 4 | 1 | no | — |
| 116 | M16×C71 | — | 4 | 1 | no | — |
| 117 | M16×C71 | — | 4 | 1 | no | — |
| 118 | M16×C71 | — | 4 | 1 | no | — |
| 119 | C2×C8×C71 | — | 2 | 2 | no | — |
| 120 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 123 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 124 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 125 | C16×C71 | — | 4 | 1 | no | — |
| 126 | C23×C71 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 127 | C22×D71 | — | 2 | 1 | no | — |
| 128 | C22×D71 | — | 4 | 1 | no | — |
| 129 | Q8×C71 | — | 4 | 1 | no | — |
| 130 | Q8×C71 | — | 4 | 1 | no | — |
| 131 | C2×C4×C71 | — | 2 | 1 | no | — |
| 132 | C2×C4×C71 | — | 2 | 1 | no | — |
| 133 | C2×C4×C71 | — | 4 | 1 | no | — |
| 134 | C2×C4×C71 | — | 4 | 1 | no | — |
| 135 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C71 | C2×D8 | 1 | 1 | yes | characteristic |
| 137 | C22⋊D71 | — | 8 | 1 | no | — |
| 138 | C22⋊D71 | — | 8 | 1 | no | — |
| 139 | C22⋊D71 | — | 8 | 1 | no | — |
| 140 | C2×Dic71 | — | 2 | 1 | no | — |
| 141 | C2×Dic71 | — | 4 | 1 | no | — |
| 142 | C2×Dic71 | — | 4 | 1 | no | — |
| 143 | C2×Dic71 | — | 4 | 1 | no | — |
| 144 | D284 | — | 4 | 1 | no | — |
| 145 | D284 | — | 4 | 1 | no | — |
| 146 | D284 | — | 4 | 1 | no | — |
| 147 | C4×D71 | — | 4 | 1 | no | — |
| 148 | C4×D71 | — | 4 | 1 | no | — |
| 149 | C4×D71 | — | 8 | 1 | no | — |
| 150 | C4×D71 | — | 8 | 2 | no | — |
| 151 | C4×D71 | — | 8 | 1 | no | — |
| 152 | Dic142 | — | 4 | 1 | no | — |
| 153 | Dic142 | — | 4 | 1 | no | — |
| 154 | Dic142 | — | 4 | 1 | no | — |
| 155 | Dic142 | — | 4 | 1 | no | — |
| 156 | Dic142 | — | 4 | 1 | no | — |
| 157 | Dic142 | — | 8 | 2 | no | — |
| 158 | C8×C71 | — | 2 | 1 | no | — |
| 159 | C8×C71 | — | 2 | 1 | no | — |
| 160 | C8×C71 | — | 4 | 2 | no | — |
| 161 | C71⋊C8 | — | 4 | 1 | no | — |
| 162 | C22×C71 | — | 2 | 1 | no | — |
| 163 | C22×C71 | — | 4 | 1 | no | — |
| 164 | C22×C71 | #447 | 1 | 1 | yes | characteristic |
| 165 | C2×D71 | — | 4 | 2 | no | — |
| 166 | C2×D71 | — | 4 | 1 | no | — |
| 167 | C2×D71 | — | 8 | 2 | no | — |
| 168 | C2×D71 | — | 8 | 1 | no | — |
| 169 | C4×C71 | — | 2 | 1 | no | — |
| 170 | C4×C71 | — | 8 | 1 | no | — |
| 171 | C4×C71 | — | 8 | 1 | no | — |
| 172 | C4×C71 | #453 | 1 | 1 | yes | characteristic |
| 173 | C4×C71 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 174 | Dic71 | — | 4 | 1 | no | — |
| 175 | Dic71 | — | 8 | 1 | no | — |
| 176 | Dic71 | — | 8 | 1 | no | — |
| 177 | Dic71 | — | 8 | 1 | no | — |
| 178 | #12118 | — | 71 | 1 | no | maximal, Sylow |
| 179 | C2×C71 | — | 2 | 1 | no | — |
| 180 | C2×C71 | — | 4 | 1 | no | — |
| 181 | C2×C71 | #1595 | 1 | 1 | yes | characteristic |
| 182 | D71 | — | 8 | 1 | no | — |
| 183 | D71 | — | 16 | 1 | no | — |
| 184 | #3202 | — | 71 | 1 | no | — |
| 185 | #2191 | — | 71 | 1 | no | — |
| 186 | #2191 | — | 71 | 1 | no | — |
| 187 | #2017 | — | 71 | 1 | no | — |
| 188 | #1342 | — | 71 | 1 | no | — |
| 189 | #1342 | D71 | 1 | 1 | yes | characteristic, complemented |
| 190 | #1321 | — | 71 | 1 | no | — |
| 191 | C71 | #12118 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 192 | #575 | — | 71 | 1 | no | — |
| 193 | #575 | — | 142 | 1 | no | — |
| 194 | #536 | — | 142 | 1 | no | — |
| 195 | #510 | — | 142 | 1 | no | — |
| 196 | #510 | — | 142 | 1 | no | — |
| 197 | #485 | — | 142 | 1 | no | — |
| 198 | #485 | — | 142 | 1 | no | — |
| 199 | #470 | — | 71 | 1 | no | — |
| 200 | #470 | C2×D71 | 1 | 1 | yes | characteristic |
| 201 | #467 | — | 142 | 1 | no | — |
| 202 | #451 | — | 142 | 1 | no | — |
| 203 | #451 | — | 142 | 1 | no | — |
| 204 | #408 | — | 71 | 1 | no | — |
| 205 | #408 | — | 142 | 1 | no | — |
| 206 | #360 | — | 142 | 1 | no | — |
| 207 | #360 | — | 142 | 1 | no | — |
| 208 | #349 | — | 71 | 1 | no | — |
| 209 | #349 | C2×D71 | 1 | 1 | yes | characteristic |
| 210 | #338 | C2×D71 | 1 | 1 | yes | characteristic |
| 211 | C2×#41 | — | 71 | 1 | no | — |
| 212 | C2×#41 | — | 142 | 1 | no | — |
| 213 | C22×Q8 | — | 142 | 1 | no | — |
| 214 | #137 | — | 284 | 1 | no | — |
| 215 | #137 | — | 284 | 1 | no | — |
| 216 | #137 | — | 284 | 1 | no | — |
| 217 | AGL(1,ℤ/8) | — | 284 | 1 | no | — |
| 218 | AGL(1,ℤ/8) | — | 284 | 1 | no | — |
| 219 | AGL(1,ℤ/8) | — | 284 | 1 | no | — |
| 220 | #135 | — | 284 | 2 | no | — |
| 221 | #135 | — | 142 | 1 | no | — |
| 222 | #135 | — | 142 | 1 | no | — |
| 223 | C2×Q16 | — | 71 | 1 | no | — |
| 224 | C2×Q16 | — | 142 | 1 | no | — |
| 225 | C2×Q16 | D284 | 1 | 1 | yes | characteristic |
| 226 | C2×M16 | — | 2 | 1 | no | — |
| 227 | C2×M16 | C22×D71 | 1 | 1 | yes | characteristic |
| 228 | C22×C8 | — | 71 | 1 | no | — |
| 229 | C4⋊Q8 | — | 284 | 1 | no | — |
| 230 | #124 | — | 284 | 1 | no | — |
| 231 | #123 | — | 284 | 1 | no | — |
| 232 | #123 | — | 284 | 1 | no | — |
| 233 | C22⋊Q8 | — | 2 | 1 | no | — |
| 234 | C22⋊Q8 | — | 142 | 1 | no | — |
| 235 | C22⋊Q8 | — | 142 | 1 | no | — |
| 236 | C22⋊Q8 | — | 142 | 1 | no | — |
| 237 | #117 | — | 142 | 1 | no | — |
| 238 | Q32 | — | 284 | 1 | no | — |
| 239 | Q32 | — | 284 | 1 | no | — |
| 240 | SD32 | — | 284 | 1 | no | — |
| 241 | SD32 | — | 284 | 1 | no | — |
| 242 | M32 | — | 2 | 1 | no | — |
| 243 | M32 | — | 142 | 1 | no | — |
| 244 | #107 | — | 142 | 1 | no | — |
| 245 | #106 | — | 71 | 1 | no | — |
| 246 | #106 | D284 | 1 | 1 | yes | characteristic |
| 247 | #103 | — | 2 | 1 | no | — |
| 248 | #103 | — | 142 | 1 | no | — |
| 249 | #103 | — | 142 | 1 | no | — |
| 250 | #103 | — | 142 | 1 | no | — |
| 251 | C22⋊C8 | — | 284 | 2 | no | — |
| 252 | C22⋊C8 | — | 142 | 1 | no | — |
| 253 | C22⋊C8 | — | 142 | 1 | no | — |
| 254 | #41 | — | 284 | 1 | no | — |
| 255 | #41 | — | 284 | 1 | no | — |
| 256 | #41 | — | 284 | 1 | no | — |
| 257 | #41 | — | 284 | 1 | no | — |
| 258 | #41 | — | 284 | 1 | no | — |
| 259 | #41 | — | 284 | 1 | no | — |
| 260 | C2×Q8 | — | 2 | 1 | no | — |
| 261 | C2×Q8 | — | 284 | 1 | no | — |
| 262 | C2×Q8 | — | 568 | 1 | no | — |
| 263 | C2×Q8 | — | 568 | 1 | no | — |
| 264 | C2×Q8 | — | 71 | 1 | no | — |
| 265 | C2×Q8 | — | 142 | 1 | no | — |
| 266 | C2×Q8 | — | 142 | 1 | no | — |
| 267 | C2×D4 | — | 284 | 1 | no | — |
| 268 | C2×D4 | — | 71 | 1 | no | — |
| 269 | C2×D4 | — | 142 | 1 | no | — |
| 270 | C2×D4 | — | 142 | 1 | no | — |
| 271 | C22×C4 | — | 284 | 1 | no | — |
| 272 | C22×C4 | — | 284 | 1 | no | — |
| 273 | C22×C4 | — | 142 | 1 | no | — |
| 274 | C22×C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 275 | Q16 | — | 4 | 1 | no | — |
| 276 | Q16 | — | 284 | 1 | no | — |
| 277 | Q16 | — | 284 | 2 | no | — |
| 278 | Q16 | — | 568 | 1 | no | — |
| 279 | Q16 | — | 142 | 1 | no | — |
| 280 | Q16 | — | 142 | 1 | no | — |
| 281 | SD16 | — | 284 | 1 | no | — |
| 282 | SD16 | — | 284 | 1 | no | — |
| 283 | SD16 | — | 284 | 2 | no | — |
| 284 | SD16 | — | 284 | 2 | no | — |
| 285 | D8 | — | 284 | 2 | no | — |
| 286 | D8 | — | 142 | 1 | no | — |
| 287 | D8 | — | 142 | 1 | no | — |
| 288 | M16 | — | 4 | 1 | no | — |
| 289 | M16 | — | 4 | 1 | no | — |
| 290 | M16 | — | 4 | 1 | no | — |
| 291 | C2×C8 | — | 2 | 2 | no | — |
| 292 | C2×C8 | — | 284 | 1 | no | — |
| 293 | C2×C8 | — | 142 | 1 | no | — |
| 294 | C2×C8 | D4×D71 | 1 | 1 | yes | characteristic |
| 295 | C2×C8 | C2×D284 | 1 | 1 | yes | characteristic |
| 296 | C4⋊C4 | — | 2 | 1 | no | — |
| 297 | C4⋊C4 | — | 4 | 1 | no | — |
| 298 | C4⋊C4 | — | 284 | 1 | no | — |
| 299 | C4⋊C4 | — | 284 | 1 | no | — |
| 300 | C4⋊C4 | — | 284 | 1 | no | — |
| 301 | C4⋊C4 | — | 142 | 1 | no | — |
| 302 | C22⋊C4 | — | 4 | 1 | no | — |
| 303 | C22⋊C4 | — | 284 | 1 | no | — |
| 304 | C22⋊C4 | — | 284 | 1 | no | — |
| 305 | C22⋊C4 | — | 284 | 1 | no | — |
| 306 | C22⋊C4 | — | 284 | 1 | no | — |
| 307 | C42 | — | 284 | 1 | no | — |
| 308 | C16 | — | 4 | 1 | no | — |
| 309 | C16 | — | 284 | 1 | no | — |
| 310 | C23 | — | 284 | 1 | no | — |
| 311 | C23 | — | 142 | 1 | no | — |
| 312 | C23 | #14556155 | 1 | 1 | yes | characteristic |
| 313 | Q8 | — | 4 | 1 | no | — |
| 314 | Q8 | — | 4 | 1 | no | — |
| 315 | Q8 | — | 284 | 1 | no | — |
| 316 | Q8 | — | 284 | 1 | no | — |
| 317 | Q8 | — | 284 | 1 | no | — |
| 318 | Q8 | — | 284 | 1 | no | — |
| 319 | Q8 | — | 284 | 1 | no | — |
| 320 | Q8 | — | 568 | 2 | no | — |
| 321 | D4 | — | 284 | 1 | no | — |
| 322 | D4 | — | 284 | 1 | no | — |
| 323 | D4 | — | 284 | 1 | no | — |
| 324 | D4 | — | 568 | 1 | no | — |
| 325 | D4 | — | 568 | 1 | no | — |
| 326 | D4 | — | 568 | 1 | no | — |
| 327 | C2×C4 | — | 2 | 1 | no | — |
| 328 | C2×C4 | — | 2 | 1 | no | — |
| 329 | C2×C4 | — | 4 | 1 | no | — |
| 330 | C2×C4 | — | 4 | 1 | no | — |
| 331 | C2×C4 | — | 284 | 1 | no | — |
| 332 | C2×C4 | — | 284 | 1 | no | — |
| 333 | C2×C4 | — | 284 | 1 | no | — |
| 334 | C2×C4 | — | 284 | 1 | no | — |
| 335 | C2×C4 | — | 284 | 1 | no | — |
| 336 | C2×C4 | — | 568 | 1 | no | — |
| 337 | C2×C4 | — | 568 | 2 | no | — |
| 338 | C2×C4 | — | 568 | 1 | no | — |
| 339 | C2×C4 | — | 142 | 1 | no | — |
| 340 | C2×C4 | #14556098 | 1 | 1 | yes | characteristic |
| 341 | C2×C4 | D8×D71 | 1 | 1 | yes | characteristic |
| 342 | C8 | — | 2 | 1 | no | — |
| 343 | C8 | — | 2 | 1 | no | — |
| 344 | C8 | — | 4 | 2 | no | — |
| 345 | C8 | — | 284 | 1 | no | — |
| 346 | C22 | — | 2 | 1 | no | — |
| 347 | C22 | — | 4 | 1 | no | — |
| 348 | C22 | — | 284 | 2 | no | — |
| 349 | C22 | — | 284 | 1 | no | — |
| 350 | C22 | — | 568 | 2 | no | — |
| 351 | C22 | — | 568 | 1 | no | — |
| 352 | C22 | #17986134 | 1 | 1 | yes | characteristic |
| 353 | C4 | — | 2 | 1 | no | — |
| 354 | C4 | — | 8 | 1 | no | — |
| 355 | C4 | — | 8 | 1 | no | — |
| 356 | C4 | — | 284 | 1 | no | — |
| 357 | C4 | — | 568 | 1 | no | — |
| 358 | C4 | — | 568 | 1 | no | — |
| 359 | C4 | — | 568 | 1 | no | — |
| 360 | C4 | #17986168 | 1 | 1 | yes | characteristic |
| 361 | C4 | #17986187 | 1 | 1 | yes | characteristic |
| 362 | C2 | — | 2 | 1 | no | — |
| 363 | C2 | — | 4 | 1 | no | — |
| 364 | C2 | — | 568 | 1 | no | — |
| 365 | C2 | — | 1136 | 1 | no | — |
| 366 | C2 | #22587259 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22599232 | C2 | semidirect |
| 2. #22590293 | C2 | semidirect |
| 3. #22590290 | C2 | semidirect |
| 5. #22586333 | C2 | semidirect |
| 6. #22586277 | C2 | semidirect |
| 7. C71×#1342 | C2 | semidirect |
| 189. #1342 | D71 | semidirect |
| 191. C71 | #12118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599232 | 2 |
| #22590293 | 2 |
| #22590290 | 2 |
| #22589445 | 2 |
| #22586333 | 2 |
| #22586277 | 2 |
| C71×#1342 | 2 |
| #12118 | 71 |