Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
442 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 57 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 | #22599200 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22590252 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22589447 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22586356 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22586355 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22586265 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C71×#2184 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14556154 | — | 2 | 1 | no | — |
| 9 | #17986565 | — | 2 | 1 | no | — |
| 10 | C2×#14556069 | — | 2 | 1 | no | — |
| 11 | #17986326 | — | 2 | 1 | no | — |
| 12 | #17986321 | — | 2 | 1 | no | — |
| 13 | #17986250 | — | 2 | 1 | no | — |
| 14 | #17986235 | C22 | 1 | 1 | yes | characteristic |
| 15 | #17986134 | — | 2 | 1 | no | — |
| 16 | #17986131 | — | 2 | 1 | no | — |
| 17 | C2×#14556045 | — | 2 | 1 | no | — |
| 18 | #17985965 | C22 | 1 | 1 | yes | characteristic |
| 19 | #17985800 | — | 2 | 1 | no | — |
| 20 | C22⋊(C71⋊C16) | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #17985764 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C22×D8×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×D16×C71 | — | 2 | 1 | no | — |
| 24 | #466×C71 | C22 | 1 | 1 | yes | characteristic |
| 25 | #357×C71 | — | 2 | 1 | no | — |
| 26 | C22⋊C16×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#11765865 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×D4×D71 | — | 2 | 1 | no | — |
| 29 | #14556154 | — | 4 | 2 | no | — |
| 30 | #14556154 | — | 4 | 2 | no | — |
| 31 | C2×#11765853 | — | 4 | 1 | no | — |
| 32 | C2×D568 | D4 | 1 | 1 | yes | characteristic |
| 33 | C2×#11765850 | — | 2 | 1 | no | — |
| 34 | C2×#11765850 | — | 4 | 1 | no | — |
| 35 | C2×#11765849 | — | 2 | 1 | no | — |
| 36 | C2×#11765849 | D4 | 1 | 1 | yes | characteristic |
| 37 | #14556124 | — | 4 | 1 | no | — |
| 38 | #14556114 | — | 4 | 1 | no | — |
| 39 | #14556103 | — | 2 | 1 | no | — |
| 40 | #14556102 | — | 2 | 1 | no | — |
| 41 | #14556099 | — | 2 | 1 | no | — |
| 42 | #14556098 | — | 4 | 1 | no | — |
| 43 | #14556096 | — | 4 | 1 | no | — |
| 44 | #14556086 | — | 2 | 1 | no | — |
| 45 | #14556069 | — | 4 | 2 | no | — |
| 46 | C2×C71⋊C16 | — | 2 | 1 | no | — |
| 47 | #14556062 | D4 | 1 | 1 | yes | characteristic |
| 48 | #14556059 | — | 2 | 1 | no | — |
| 49 | #14556050 | — | 2 | 1 | no | — |
| 50 | #14556049 | — | 2 | 1 | no | — |
| 51 | #14556048 | — | 2 | 1 | no | — |
| 52 | #14556045 | — | 4 | 2 | no | — |
| 53 | (C2×D71)⋊C8 | — | 2 | 1 | no | — |
| 54 | (C2×D71)⋊C8 | — | 2 | 1 | no | — |
| 55 | C22×D4×C71 | — | 2 | 1 | no | — |
| 56 | C2×D8×C71 | — | 2 | 1 | no | — |
| 57 | C2×D8×C71 | — | 2 | 1 | no | — |
| 58 | C2×D8×C71 | — | 4 | 2 | no | — |
| 59 | C2×D8×C71 | D4 | 1 | 1 | yes | characteristic |
| 60 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 61 | #121×C71 | — | 2 | 1 | no | — |
| 62 | D16×C71 | — | 4 | 2 | no | — |
| 63 | C2×C16×C71 | — | 2 | 1 | no | — |
| 64 | #107×C71 | D4 | 1 | 1 | yes | characteristic |
| 65 | #102×C71 | — | 2 | 1 | no | — |
| 66 | C23×D71 | — | 4 | 1 | no | — |
| 67 | #11765865 | — | 4 | 1 | no | — |
| 68 | #11765865 | — | 4 | 1 | no | — |
| 69 | C2×Dic142 | D8 | 1 | 1 | yes | characteristic |
| 70 | C2×D284 | — | 2 | 1 | no | — |
| 71 | C2×D284 | — | 4 | 1 | no | — |
| 72 | C2×D284 | D8 | 1 | 1 | yes | characteristic |
| 73 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 74 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 75 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 76 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 77 | D4×D71 | — | 8 | 1 | no | — |
| 78 | D4×D71 | — | 8 | 1 | no | — |
| 79 | C2×C4×D71 | — | 2 | 1 | no | — |
| 80 | #11765853 | — | 4 | 4 | no | — |
| 81 | D568 | — | 4 | 1 | no | — |
| 82 | #11765850 | — | 4 | 4 | no | — |
| 83 | #11765850 | — | 8 | 1 | no | — |
| 84 | #11765849 | — | 2 | 2 | no | — |
| 85 | #11765849 | — | 4 | 1 | no | — |
| 86 | #11765849 | — | 4 | 1 | no | — |
| 87 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 88 | C2×C71⋊C8 | — | 4 | 1 | no | — |
| 89 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 90 | C22⋊Dic71 | — | 4 | 1 | no | — |
| 91 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 92 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 93 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 94 | C4×Dic71 | — | 4 | 1 | no | — |
| 95 | C71⋊C16 | — | 4 | 1 | no | — |
| 96 | C24×C71 | — | 4 | 1 | no | — |
| 97 | C2×D4×C71 | — | 2 | 2 | no | — |
| 98 | C2×D4×C71 | — | 2 | 1 | no | — |
| 99 | C2×D4×C71 | — | 4 | 1 | no | — |
| 100 | C2×D4×C71 | — | 4 | 1 | no | — |
| 101 | C2×D4×C71 | — | 4 | 1 | no | — |
| 102 | C2×D4×C71 | — | 4 | 1 | no | — |
| 103 | C2×D4×C71 | — | 4 | 1 | no | — |
| 104 | C2×D4×C71 | — | 4 | 1 | no | — |
| 105 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | D8×C71 | — | 2 | 2 | no | — |
| 107 | D8×C71 | — | 2 | 2 | no | — |
| 108 | D8×C71 | — | 4 | 1 | no | — |
| 109 | D8×C71 | — | 4 | 1 | no | — |
| 110 | D8×C71 | — | 4 | 1 | no | — |
| 111 | C2×C8×C71 | — | 4 | 1 | no | — |
| 112 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 115 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 116 | C16×C71 | — | 4 | 1 | no | — |
| 117 | C23×C71 | — | 4 | 2 | no | — |
| 118 | C23×C71 | — | 4 | 1 | no | — |
| 119 | C23×C71 | — | 8 | 1 | no | — |
| 120 | C23×C71 | — | 8 | 1 | no | — |
| 121 | C23×C71 | — | 16 | 1 | no | — |
| 122 | C23×C71 | — | 16 | 1 | no | — |
| 123 | C23×C71 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 124 | C22×D71 | — | 2 | 1 | no | — |
| 125 | C22×D71 | — | 4 | 1 | no | — |
| 126 | C22×D71 | — | 8 | 2 | no | — |
| 127 | C22×D71 | — | 16 | 1 | no | — |
| 128 | C22×D71 | — | 16 | 1 | no | — |
| 129 | D4×C71 | — | 4 | 2 | no | — |
| 130 | D4×C71 | — | 4 | 1 | no | — |
| 131 | D4×C71 | — | 4 | 2 | no | — |
| 132 | D4×C71 | — | 4 | 1 | no | — |
| 133 | D4×C71 | — | 8 | 1 | no | — |
| 134 | D4×C71 | — | 8 | 1 | no | — |
| 135 | D4×C71 | — | 16 | 1 | no | — |
| 136 | C2×C4×C71 | — | 2 | 1 | no | — |
| 137 | C2×C4×C71 | — | 2 | 1 | no | — |
| 138 | C2×C4×C71 | — | 4 | 1 | no | — |
| 139 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 140 | C2×C4×C71 | C2×D8 | 1 | 1 | yes | characteristic |
| 141 | C22⋊D71 | — | 8 | 1 | no | — |
| 142 | C22⋊D71 | — | 8 | 2 | no | — |
| 143 | C22⋊D71 | — | 16 | 1 | no | — |
| 144 | C22⋊D71 | — | 16 | 1 | no | — |
| 145 | C2×Dic71 | — | 2 | 1 | no | — |
| 146 | C2×Dic71 | — | 4 | 1 | no | — |
| 147 | D284 | — | 4 | 1 | no | — |
| 148 | D284 | — | 4 | 1 | no | — |
| 149 | D284 | — | 4 | 1 | no | — |
| 150 | D284 | — | 16 | 1 | no | — |
| 151 | C4×D71 | — | 4 | 1 | no | — |
| 152 | C4×D71 | — | 4 | 1 | no | — |
| 153 | Dic142 | — | 4 | 1 | no | — |
| 154 | C8×C71 | — | 2 | 1 | no | — |
| 155 | C8×C71 | — | 2 | 1 | no | — |
| 156 | C71⋊C8 | — | 4 | 2 | no | — |
| 157 | C71⋊C8 | — | 4 | 1 | no | — |
| 158 | C22×C71 | — | 2 | 1 | no | — |
| 159 | C22×C71 | — | 2 | 1 | no | — |
| 160 | C22×C71 | — | 2 | 1 | no | — |
| 161 | C22×C71 | — | 8 | 1 | no | — |
| 162 | C22×C71 | — | 8 | 2 | no | — |
| 163 | C22×C71 | — | 8 | 1 | no | — |
| 164 | C22×C71 | — | 8 | 1 | no | — |
| 165 | C22×C71 | — | 16 | 2 | no | — |
| 166 | C22×C71 | — | 16 | 2 | no | — |
| 167 | C22×C71 | — | 16 | 1 | no | — |
| 168 | C22×C71 | — | 16 | 1 | no | — |
| 169 | C22×C71 | #447 | 1 | 1 | yes | characteristic |
| 170 | C2×D71 | — | 4 | 1 | no | — |
| 171 | C2×D71 | — | 4 | 1 | no | — |
| 172 | C2×D71 | — | 4 | 1 | no | — |
| 173 | C2×D71 | — | 8 | 1 | no | — |
| 174 | C2×D71 | — | 8 | 1 | no | — |
| 175 | C2×D71 | — | 8 | 1 | no | — |
| 176 | C2×D71 | — | 16 | 4 | no | — |
| 177 | C4×C71 | — | 2 | 1 | no | — |
| 178 | C4×C71 | — | 8 | 1 | no | — |
| 179 | C4×C71 | #453 | 1 | 1 | yes | characteristic |
| 180 | C4×C71 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 181 | Dic71 | — | 4 | 1 | no | — |
| 182 | Dic71 | — | 8 | 1 | no | — |
| 183 | #12108 | — | 71 | 1 | no | maximal, Sylow |
| 184 | C2×C71 | — | 4 | 1 | no | — |
| 185 | C2×C71 | — | 16 | 1 | no | — |
| 186 | C2×C71 | — | 16 | 2 | no | — |
| 187 | C2×C71 | #1595 | 1 | 1 | yes | characteristic |
| 188 | C2×C71 | #2192 | 1 | 1 | yes | characteristic |
| 189 | C2×C71 | #2192 | 1 | 1 | yes | characteristic |
| 190 | D71 | — | 8 | 1 | no | — |
| 191 | D71 | — | 16 | 1 | no | — |
| 192 | #3199 | — | 71 | 1 | no | — |
| 193 | #2184 | — | 71 | 1 | no | — |
| 194 | #2184 | D71 | 1 | 1 | yes | characteristic, complemented |
| 195 | #2018 | — | 71 | 1 | no | — |
| 196 | #1349 | — | 71 | 1 | no | — |
| 197 | #1349 | — | 71 | 1 | no | — |
| 198 | #1315 | — | 71 | 1 | no | — |
| 199 | C71 | #12108 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 200 | C2×AGL(1,ℤ/8) | — | 142 | 1 | no | — |
| 201 | C22×D8 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 202 | #535 | — | 142 | 1 | no | — |
| 203 | C2×D16 | — | 2 | 1 | no | — |
| 204 | C2×D16 | — | 142 | 1 | no | — |
| 205 | #482 | — | 142 | 1 | no | — |
| 206 | #482 | — | 142 | 1 | no | — |
| 207 | #469 | — | 142 | 1 | no | — |
| 208 | #466 | — | 71 | 1 | no | — |
| 209 | #466 | C2×D71 | 1 | 1 | yes | characteristic |
| 210 | #447 | — | 142 | 1 | no | — |
| 211 | #447 | — | 142 | 1 | no | — |
| 212 | C2×#100 | — | 142 | 1 | no | — |
| 213 | #408 | — | 71 | 1 | no | — |
| 214 | #357 | — | 2 | 1 | no | — |
| 215 | #357 | — | 142 | 1 | no | — |
| 216 | C22⋊C16 | — | 71 | 1 | no | — |
| 217 | C22⋊C16 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 218 | #341 | — | 71 | 1 | no | — |
| 219 | C2×#41 | — | 71 | 1 | no | — |
| 220 | C22×D4 | — | 2 | 1 | no | — |
| 221 | C22×D4 | — | 142 | 1 | no | — |
| 222 | AGL(1,ℤ/8) | — | 284 | 2 | no | — |
| 223 | AGL(1,ℤ/8) | — | 284 | 2 | no | — |
| 224 | C2×SD16 | — | 284 | 1 | no | — |
| 225 | C2×D8 | — | 2 | 1 | no | — |
| 226 | C2×D8 | — | 2 | 1 | no | — |
| 227 | C2×D8 | — | 4 | 2 | no | — |
| 228 | C2×D8 | — | 284 | 1 | no | — |
| 229 | C2×D8 | — | 71 | 1 | no | — |
| 230 | C2×D8 | — | 142 | 1 | no | — |
| 231 | C2×D8 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 232 | C2×M16 | — | 71 | 1 | no | — |
| 233 | C2×M16 | — | 142 | 1 | no | — |
| 234 | C22×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 235 | #127 | — | 284 | 1 | no | — |
| 236 | #124 | — | 284 | 1 | no | — |
| 237 | #121 | — | 2 | 1 | no | — |
| 238 | #121 | — | 142 | 1 | no | — |
| 239 | #121 | — | 142 | 1 | no | — |
| 240 | #121 | — | 142 | 1 | no | — |
| 241 | #120 | — | 284 | 1 | no | — |
| 242 | #120 | — | 284 | 1 | no | — |
| 243 | #117 | — | 142 | 1 | no | — |
| 244 | D16 | — | 4 | 2 | no | — |
| 245 | D16 | — | 284 | 2 | no | — |
| 246 | C2×C16 | — | 2 | 1 | no | — |
| 247 | C2×C16 | — | 142 | 1 | no | — |
| 248 | #107 | — | 71 | 1 | no | — |
| 249 | #107 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 250 | #106 | — | 142 | 1 | no | — |
| 251 | #102 | — | 2 | 1 | no | — |
| 252 | #102 | — | 142 | 1 | no | — |
| 253 | #102 | — | 142 | 1 | no | — |
| 254 | #102 | — | 142 | 1 | no | — |
| 255 | #100 | — | 284 | 2 | no | — |
| 256 | C22⋊C8 | — | 142 | 1 | no | — |
| 257 | C22⋊C8 | — | 142 | 1 | no | — |
| 258 | C24 | — | 4 | 1 | no | — |
| 259 | C24 | — | 284 | 1 | no | — |
| 260 | #41 | — | 284 | 1 | no | — |
| 261 | #41 | — | 284 | 1 | no | — |
| 262 | C2×Q8 | — | 71 | 1 | no | — |
| 263 | C2×D4 | — | 2 | 2 | no | — |
| 264 | C2×D4 | — | 2 | 1 | no | — |
| 265 | C2×D4 | — | 4 | 1 | no | — |
| 266 | C2×D4 | — | 4 | 1 | no | — |
| 267 | C2×D4 | — | 4 | 1 | no | — |
| 268 | C2×D4 | — | 4 | 1 | no | — |
| 269 | C2×D4 | — | 4 | 1 | no | — |
| 270 | C2×D4 | — | 4 | 1 | no | — |
| 271 | C2×D4 | — | 284 | 1 | no | — |
| 272 | C2×D4 | — | 284 | 1 | no | — |
| 273 | C2×D4 | — | 284 | 1 | no | — |
| 274 | C2×D4 | — | 284 | 1 | no | — |
| 275 | C2×D4 | — | 568 | 1 | no | — |
| 276 | C2×D4 | — | 568 | 1 | no | — |
| 277 | C2×D4 | — | 71 | 1 | no | — |
| 278 | C2×D4 | — | 142 | 1 | no | — |
| 279 | C2×D4 | — | 142 | 1 | no | — |
| 280 | C22×C4 | — | 142 | 1 | no | — |
| 281 | C22×C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 282 | SD16 | — | 284 | 4 | no | — |
| 283 | D8 | — | 2 | 2 | no | — |
| 284 | D8 | — | 2 | 2 | no | — |
| 285 | D8 | — | 4 | 1 | no | — |
| 286 | D8 | — | 4 | 1 | no | — |
| 287 | D8 | — | 4 | 1 | no | — |
| 288 | D8 | — | 284 | 1 | no | — |
| 289 | D8 | — | 284 | 4 | no | — |
| 290 | D8 | — | 568 | 1 | no | — |
| 291 | M16 | — | 284 | 1 | no | — |
| 292 | M16 | — | 284 | 1 | no | — |
| 293 | M16 | — | 142 | 2 | no | — |
| 294 | C2×C8 | — | 4 | 1 | no | — |
| 295 | C2×C8 | — | 284 | 1 | no | — |
| 296 | C2×C8 | — | 142 | 1 | no | — |
| 297 | C2×C8 | D4×D71 | 1 | 1 | yes | characteristic |
| 298 | C2×C8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 299 | C4⋊C4 | — | 2 | 1 | no | — |
| 300 | C4⋊C4 | — | 142 | 1 | no | — |
| 301 | C22⋊C4 | — | 4 | 1 | no | — |
| 302 | C22⋊C4 | — | 284 | 1 | no | — |
| 303 | C22⋊C4 | — | 284 | 1 | no | — |
| 304 | C22⋊C4 | — | 284 | 1 | no | — |
| 305 | C22⋊C4 | — | 284 | 1 | no | — |
| 306 | C42 | — | 284 | 1 | no | — |
| 307 | C16 | — | 4 | 1 | no | — |
| 308 | C16 | — | 284 | 1 | no | — |
| 309 | C23 | — | 4 | 2 | no | — |
| 310 | C23 | — | 4 | 1 | no | — |
| 311 | C23 | — | 8 | 1 | no | — |
| 312 | C23 | — | 8 | 1 | no | — |
| 313 | C23 | — | 16 | 1 | no | — |
| 314 | C23 | — | 16 | 1 | no | — |
| 315 | C23 | — | 284 | 1 | no | — |
| 316 | C23 | — | 568 | 2 | no | — |
| 317 | C23 | — | 1136 | 1 | no | — |
| 318 | C23 | — | 1136 | 1 | no | — |
| 319 | C23 | — | 142 | 1 | no | — |
| 320 | C23 | #14556152 | 1 | 1 | yes | characteristic |
| 321 | Q8 | — | 284 | 1 | no | — |
| 322 | D4 | — | 4 | 2 | no | — |
| 323 | D4 | — | 4 | 1 | no | — |
| 324 | D4 | — | 4 | 2 | no | — |
| 325 | D4 | — | 4 | 1 | no | — |
| 326 | D4 | — | 8 | 1 | no | — |
| 327 | D4 | — | 8 | 1 | no | — |
| 328 | D4 | — | 16 | 1 | no | — |
| 329 | D4 | — | 284 | 1 | no | — |
| 330 | D4 | — | 284 | 1 | no | — |
| 331 | D4 | — | 284 | 1 | no | — |
| 332 | D4 | — | 568 | 1 | no | — |
| 333 | D4 | — | 568 | 2 | no | — |
| 334 | D4 | — | 1136 | 1 | no | — |
| 335 | D4 | — | 1136 | 1 | no | — |
| 336 | D4 | — | 1136 | 1 | no | — |
| 337 | C2×C4 | — | 2 | 1 | no | — |
| 338 | C2×C4 | — | 2 | 1 | no | — |
| 339 | C2×C4 | — | 4 | 1 | no | — |
| 340 | C2×C4 | — | 284 | 1 | no | — |
| 341 | C2×C4 | — | 284 | 1 | no | — |
| 342 | C2×C4 | — | 284 | 1 | no | — |
| 343 | C2×C4 | — | 142 | 1 | no | — |
| 344 | C2×C4 | #14556096 | 1 | 1 | yes | characteristic |
| 345 | C2×C4 | D8×D71 | 1 | 1 | yes | characteristic |
| 346 | C8 | — | 2 | 1 | no | — |
| 347 | C8 | — | 2 | 1 | no | — |
| 348 | C8 | — | 284 | 2 | no | — |
| 349 | C8 | — | 284 | 1 | no | — |
| 350 | C22 | — | 2 | 1 | no | — |
| 351 | C22 | — | 2 | 1 | no | — |
| 352 | C22 | — | 2 | 1 | no | — |
| 353 | C22 | — | 8 | 1 | no | — |
| 354 | C22 | — | 8 | 1 | no | — |
| 355 | C22 | — | 8 | 2 | no | — |
| 356 | C22 | — | 8 | 1 | no | — |
| 357 | C22 | — | 16 | 2 | no | — |
| 358 | C22 | — | 16 | 2 | no | — |
| 359 | C22 | — | 16 | 1 | no | — |
| 360 | C22 | — | 16 | 1 | no | — |
| 361 | C22 | — | 284 | 1 | no | — |
| 362 | C22 | — | 284 | 1 | no | — |
| 363 | C22 | — | 284 | 1 | no | — |
| 364 | C22 | — | 568 | 1 | no | — |
| 365 | C22 | — | 568 | 1 | no | — |
| 366 | C22 | — | 568 | 1 | no | — |
| 367 | C22 | — | 1136 | 4 | no | — |
| 368 | C22 | #17986131 | 1 | 1 | yes | characteristic |
| 369 | C4 | — | 2 | 1 | no | — |
| 370 | C4 | — | 8 | 1 | no | — |
| 371 | C4 | — | 284 | 1 | no | — |
| 372 | C4 | — | 568 | 1 | no | — |
| 373 | C4 | #17986165 | 1 | 1 | yes | characteristic |
| 374 | C4 | #17986185 | 1 | 1 | yes | characteristic |
| 375 | C2 | — | 4 | 1 | no | — |
| 376 | C2 | — | 16 | 1 | no | — |
| 377 | C2 | — | 16 | 2 | no | — |
| 378 | C2 | — | 568 | 1 | no | — |
| 379 | C2 | — | 1136 | 1 | no | — |
| 380 | C2 | #22587256 | 1 | 1 | yes | characteristic |
| 381 | C2 | #22590294 | 1 | 1 | yes | characteristic |
| 382 | C2 | #22590296 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22599200 | C2 | semidirect |
| 2. #22590252 | C2 | semidirect |
| 3. #22589447 | C2 | semidirect |
| 4. #22586356 | C2 | semidirect |
| 5. #22586355 | C2 | semidirect |
| 6. #22586265 | C2 | semidirect |
| 7. C71×#2184 | C2 | semidirect |
| 20. C22⋊(C71⋊C16) | C22 | semidirect |
| 21. #17985764 | C22 | semidirect |
| 22. C22×D8×C71 | C22 | semidirect |
| 26. C22⋊C16×C71 | C22 | semidirect |
| 194. #2184 | D71 | semidirect |
| 199. C71 | #12108 | semidirect |
| 201. C22×D8 | C2×D71 | semidirect |
| 217. C22⋊C16 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599200 | 2 |
| #22590252 | 2 |
| #22589447 | 2 |
| #22586356 | 2 |
| #22586355 | 2 |
| #22586265 | 2 |
| C71×#2184 | 2 |
| #12108 | 71 |