Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
924 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 119 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 | #22602120 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22589328 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22586932 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22586777 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C71×#1560 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#14556175 | C4 | 1 | 2 | yes | — |
| 7 | D4×Dic142 | — | 2 | 2 | no | — |
| 8 | #17986654 | — | 2 | 2 | no | — |
| 9 | #17986649 | — | 2 | 4 | no | — |
| 10 | #17986570 | C4 | 1 | 2 | yes | — |
| 11 | #17986569 | — | 2 | 2 | no | — |
| 12 | #17986547 | — | 2 | 1 | no | — |
| 13 | C2×#14556128 | C22 | 1 | 1 | yes | characteristic |
| 14 | C4⋊Q8×D71 | — | 2 | 1 | no | — |
| 15 | C4×#11765865 | C22 | 1 | 1 | yes | characteristic |
| 16 | C4×#11765849 | C22 | 1 | 2 | yes | — |
| 17 | #17985767 | — | 2 | 4 | no | — |
| 18 | #17985739 | — | 2 | 2 | no | — |
| 19 | #17985729 | — | 2 | 2 | no | — |
| 20 | #17985726 | — | 2 | 2 | no | — |
| 21 | #532×C71 | C22 | 1 | 1 | yes | characteristic |
| 22 | #423×C71 | C22 | 1 | 2 | yes | — |
| 23 | #333×C71 | — | 2 | 1 | no | — |
| 24 | #331×C71 | — | 2 | 1 | no | — |
| 25 | #14556175 | — | 4 | 4 | no | — |
| 26 | #14556175 | — | 4 | 4 | no | — |
| 27 | C2×#11765865 | — | 2 | 2 | no | — |
| 28 | C2×#11765865 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | C2×#11765864 | — | 2 | 4 | no | — |
| 30 | C2×#11765864 | — | 2 | 2 | no | — |
| 31 | C22×Dic142 | — | 2 | 2 | no | — |
| 32 | C22×Dic142 | C2×C4 | 1 | 2 | yes | — |
| 33 | C2×Q8×D71 | — | 2 | 2 | no | — |
| 34 | C2×#11765849 | — | 2 | 2 | no | — |
| 35 | #14556128 | — | 2 | 1 | no | — |
| 36 | #14556128 | — | 2 | 2 | no | — |
| 37 | #14556128 | — | 2 | 1 | no | — |
| 38 | #14556127 | — | 2 | 4 | no | — |
| 39 | #14556126 | — | 2 | 2 | no | — |
| 40 | #14556115 | — | 2 | 2 | no | — |
| 41 | #14556110 | — | 2 | 8 | no | — |
| 42 | #14556109 | — | 2 | 4 | no | — |
| 43 | #14556107 | — | 2 | 4 | no | — |
| 44 | #14556105 | — | 2 | 8 | no | — |
| 45 | #14556099 | — | 2 | 4 | no | — |
| 46 | C4×Dic142 | D4 | 1 | 2 | yes | — |
| 47 | C4×D284 | D4 | 1 | 2 | yes | — |
| 48 | D4×Dic71 | — | 2 | 4 | no | — |
| 49 | C4×C22⋊D71 | — | 2 | 2 | no | — |
| 50 | #14556087 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | #14556085 | — | 2 | 1 | no | — |
| 52 | C2×C4⋊Dic71 | D4 | 1 | 4 | yes | — |
| 53 | C4⋊C4×D71 | — | 2 | 4 | no | — |
| 54 | C42×D71 | — | 2 | 1 | no | — |
| 55 | #14556039 | — | 2 | 2 | no | — |
| 56 | C4×C71⋊C8 | — | 2 | 2 | no | — |
| 57 | C2×#41×C71 | C2×C4 | 1 | 2 | yes | — |
| 58 | C2×M16×C71 | — | 2 | 2 | no | — |
| 59 | C4⋊Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 60 | #127×C71 | D4 | 1 | 1 | yes | characteristic |
| 61 | #124×C71 | D4 | 1 | 2 | yes | — |
| 62 | #121×C71 | — | 2 | 2 | no | — |
| 63 | C4×D4×C71 | — | 2 | 2 | no | — |
| 64 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 65 | C4⋊C8×C71 | — | 2 | 2 | no | — |
| 66 | C4⋊C8×C71 | — | 2 | 2 | no | — |
| 67 | #11765865 | — | 2 | 2 | no | — |
| 68 | #11765865 | — | 2 | 2 | no | — |
| 69 | #11765865 | — | 4 | 4 | no | — |
| 70 | #11765865 | — | 4 | 4 | no | — |
| 71 | #11765864 | — | 4 | 8 | no | — |
| 72 | #11765864 | — | 4 | 16 | no | — |
| 73 | C2×Dic142 | — | 2 | 4 | no | — |
| 74 | C2×Dic142 | — | 2 | 2 | no | — |
| 75 | C2×Dic142 | — | 2 | 2 | no | — |
| 76 | C2×Dic142 | — | 4 | 4 | no | — |
| 77 | C2×Dic142 | — | 4 | 4 | no | — |
| 78 | C2×Dic142 | — | 4 | 2 | no | — |
| 79 | C2×Dic142 | — | 4 | 2 | no | — |
| 80 | C2×Dic142 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 81 | Q8×D71 | — | 4 | 8 | no | — |
| 82 | C2×D284 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 83 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 84 | C2×C22⋊D71 | — | 2 | 4 | no | — |
| 85 | C22×Dic71 | — | 2 | 4 | no | — |
| 86 | C22×Dic71 | C22⋊C4 | 1 | 4 | yes | — |
| 87 | C2×C4×D71 | — | 2 | 1 | no | — |
| 88 | C2×C4×D71 | — | 2 | 4 | no | — |
| 89 | C2×C4×D71 | — | 2 | 2 | no | — |
| 90 | #11765849 | — | 2 | 4 | no | — |
| 91 | #11765849 | — | 4 | 2 | no | — |
| 92 | C2×C71⋊C8 | — | 4 | 2 | no | — |
| 93 | C4⋊Dic71 | — | 2 | 4 | no | — |
| 94 | C4⋊Dic71 | — | 2 | 4 | no | — |
| 95 | C4⋊Dic71 | C22⋊C4 | 1 | 2 | yes | — |
| 96 | Dic71⋊C4 | — | 2 | 8 | no | — |
| 97 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 98 | C22⋊Dic71 | — | 2 | 8 | no | — |
| 99 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 100 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 101 | C4×Dic71 | — | 2 | 1 | no | — |
| 102 | C4×Dic71 | — | 2 | 2 | no | — |
| 103 | #41×C71 | — | 4 | 2 | no | — |
| 104 | #41×C71 | — | 4 | 2 | no | — |
| 105 | C2×Q8×C71 | C22⋊C4 | 1 | 2 | yes | — |
| 106 | C2×D4×C71 | — | 2 | 2 | no | — |
| 107 | C2×D4×C71 | — | 2 | 2 | no | — |
| 108 | C2×D4×C71 | C22⋊C4 | 1 | 2 | yes | — |
| 109 | C22×C4×C71 | — | 2 | 2 | no | — |
| 110 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 111 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 112 | M16×C71 | — | 4 | 4 | no | — |
| 113 | C2×C8×C71 | — | 4 | 2 | no | — |
| 114 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 115 | C22⋊C4×C71 | — | 2 | 4 | no | — |
| 116 | C42×C71 | C2×D4 | 1 | 2 | yes | — |
| 117 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C23×C71 | — | 2 | 2 | no | — |
| 120 | C23×C71 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 121 | C22×D71 | — | 2 | 1 | no | — |
| 122 | Q8×C71 | — | 4 | 2 | no | — |
| 123 | D4×C71 | — | 4 | 2 | no | — |
| 124 | D4×C71 | — | 4 | 4 | no | — |
| 125 | D4×C71 | — | 4 | 2 | no | — |
| 126 | D4×C71 | — | 4 | 2 | no | — |
| 127 | C2×C4×C71 | — | 2 | 1 | no | — |
| 128 | C2×C4×C71 | — | 2 | 1 | no | — |
| 129 | C2×C4×C71 | — | 2 | 2 | no | — |
| 130 | C2×C4×C71 | — | 2 | 2 | no | — |
| 131 | C2×C4×C71 | — | 2 | 2 | no | — |
| 132 | C2×C4×C71 | — | 4 | 2 | no | — |
| 133 | C2×C4×C71 | — | 4 | 2 | no | — |
| 134 | C2×C4×C71 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 135 | C2×C4×C71 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C71 | #120 | 1 | 2 | yes | — |
| 137 | C2×C4×C71 | #120 | 1 | 2 | yes | — |
| 138 | C22⋊D71 | — | 2 | 4 | no | — |
| 139 | C22⋊D71 | — | 4 | 8 | no | — |
| 140 | C2×Dic71 | — | 2 | 1 | no | — |
| 141 | C2×Dic71 | — | 2 | 2 | no | — |
| 142 | C2×Dic71 | — | 2 | 4 | no | — |
| 143 | C2×Dic71 | — | 4 | 8 | no | — |
| 144 | C2×Dic71 | — | 4 | 4 | no | — |
| 145 | D284 | — | 2 | 1 | no | — |
| 146 | D284 | #100 | 1 | 2 | yes | — |
| 147 | C4×D71 | — | 2 | 4 | no | — |
| 148 | C4×D71 | — | 4 | 8 | no | — |
| 149 | C4×D71 | — | 4 | 2 | no | — |
| 150 | C4×D71 | — | 4 | 2 | no | — |
| 151 | Dic142 | — | 2 | 1 | no | — |
| 152 | Dic142 | — | 4 | 8 | no | — |
| 153 | Dic142 | — | 4 | 4 | no | — |
| 154 | Dic142 | — | 4 | 2 | no | — |
| 155 | Dic142 | — | 4 | 2 | no | — |
| 156 | Dic142 | #100 | 1 | 2 | yes | — |
| 157 | C8×C71 | — | 8 | 2 | no | — |
| 158 | C71⋊C8 | — | 4 | 4 | no | — |
| 159 | C22×C71 | — | 2 | 2 | no | — |
| 160 | C22×C71 | — | 2 | 1 | no | — |
| 161 | C22×C71 | — | 4 | 4 | no | — |
| 162 | C22×C71 | — | 4 | 2 | no | — |
| 163 | C22×C71 | #379 | 1 | 1 | yes | characteristic |
| 164 | C2×D71 | — | 2 | 2 | no | — |
| 165 | C2×D71 | — | 4 | 2 | no | — |
| 166 | C4×C71 | — | 2 | 2 | no | — |
| 167 | C4×C71 | — | 2 | 1 | no | — |
| 168 | C4×C71 | — | 4 | 2 | no | — |
| 169 | C4×C71 | C2×#100 | 1 | 1 | yes | characteristic |
| 170 | C4×C71 | C2×#100 | 1 | 1 | yes | characteristic |
| 171 | C4×C71 | #454 | 1 | 2 | yes | — |
| 172 | C4×C71 | #456 | 1 | 2 | yes | — |
| 173 | Dic71 | — | 2 | 2 | no | — |
| 174 | Dic71 | — | 4 | 2 | no | — |
| 175 | Dic71 | — | 4 | 4 | no | — |
| 176 | #8471 | — | 71 | 1 | no | maximal, Sylow |
| 177 | C2×C71 | — | 4 | 1 | no | — |
| 178 | C2×C71 | — | 8 | 2 | no | — |
| 179 | C2×C71 | #1783 | 1 | 1 | yes | characteristic |
| 180 | C2×C71 | #1793 | 1 | 2 | yes | — |
| 181 | D71 | — | 4 | 2 | no | — |
| 182 | #3499 | — | 71 | 1 | no | — |
| 183 | #1997 | — | 71 | 2 | no | — |
| 184 | #1560 | D71 | 1 | 1 | yes | characteristic, complemented |
| 185 | #1525 | — | 71 | 1 | no | — |
| 186 | #1489 | — | 71 | 2 | no | — |
| 187 | C71 | #8471 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 188 | C2×2−1+4 | — | 71 | 2 | no | — |
| 189 | D4×Q8 | — | 142 | 2 | no | — |
| 190 | #547 | — | 142 | 4 | no | — |
| 191 | #547 | — | 142 | 2 | no | — |
| 192 | #536 | — | 71 | 2 | no | — |
| 193 | #536 | — | 142 | 2 | no | — |
| 194 | #532 | — | 142 | 1 | no | — |
| 195 | #532 | C2×D71 | 1 | 1 | yes | characteristic |
| 196 | C2×C4⋊Q8 | — | 71 | 1 | no | — |
| 197 | C2×C4⋊Q8 | — | 142 | 1 | no | — |
| 198 | C4×#41 | — | 71 | 1 | no | — |
| 199 | #423 | C2×D71 | 1 | 2 | yes | — |
| 200 | C4×M16 | — | 71 | 2 | no | — |
| 201 | #343 | — | 142 | 4 | no | — |
| 202 | #333 | — | 2 | 1 | no | — |
| 203 | #331 | — | 2 | 1 | no | — |
| 204 | #329 | — | 142 | 2 | no | — |
| 205 | Q8⋊C8 | — | 142 | 2 | no | — |
| 206 | D4⋊C8 | — | 142 | 2 | no | — |
| 207 | 2−1+4 | — | 284 | 4 | no | — |
| 208 | 2−1+4 | — | 284 | 4 | no | — |
| 209 | C2×#41 | — | 71 | 1 | no | — |
| 210 | C2×#41 | — | 142 | 2 | no | — |
| 211 | C2×#41 | — | 142 | 4 | no | — |
| 212 | C2×#41 | — | 142 | 2 | no | — |
| 213 | C2×#41 | C4×D71 | 1 | 2 | yes | — |
| 214 | C22×Q8 | — | 71 | 2 | no | — |
| 215 | C22×Q8 | — | 142 | 2 | no | — |
| 216 | C22×Q8 | — | 142 | 2 | no | — |
| 217 | C2×M16 | — | 2 | 2 | no | — |
| 218 | C2×M16 | — | 142 | 2 | no | — |
| 219 | C4⋊Q8 | — | 142 | 4 | no | — |
| 220 | C4⋊Q8 | — | 142 | 2 | no | — |
| 221 | C4⋊Q8 | — | 142 | 2 | no | — |
| 222 | C4⋊Q8 | — | 142 | 1 | no | — |
| 223 | C4⋊Q8 | — | 142 | 1 | no | — |
| 224 | C4⋊Q8 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 225 | #127 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 226 | #124 | — | 142 | 2 | no | — |
| 227 | #124 | D284 | 1 | 2 | yes | — |
| 228 | #123 | — | 142 | 8 | no | — |
| 229 | #123 | — | 142 | 4 | no | — |
| 230 | C22⋊Q8 | — | 142 | 8 | no | — |
| 231 | C22⋊Q8 | — | 142 | 4 | no | — |
| 232 | #121 | — | 2 | 2 | no | — |
| 233 | #121 | — | 142 | 4 | no | — |
| 234 | C4×Q8 | — | 71 | 2 | no | — |
| 235 | C4×D4 | — | 2 | 2 | no | — |
| 236 | C4×D4 | — | 71 | 2 | no | — |
| 237 | C4×D4 | — | 142 | 4 | no | — |
| 238 | C4×D4 | — | 142 | 2 | no | — |
| 239 | #117 | — | 71 | 1 | no | — |
| 240 | #117 | — | 142 | 1 | no | — |
| 241 | C2×C4⋊C4 | — | 71 | 4 | no | — |
| 242 | C2×C4⋊C4 | — | 142 | 4 | no | — |
| 243 | C2×C42 | — | 142 | 1 | no | — |
| 244 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 245 | C4⋊C8 | — | 2 | 2 | no | — |
| 246 | C4⋊C8 | — | 2 | 2 | no | — |
| 247 | #97 | — | 142 | 2 | no | — |
| 248 | C4×C8 | — | 142 | 2 | no | — |
| 249 | #41 | — | 4 | 2 | no | — |
| 250 | #41 | — | 4 | 2 | no | — |
| 251 | #41 | — | 284 | 4 | no | — |
| 252 | #41 | — | 284 | 4 | no | — |
| 253 | #41 | — | 284 | 16 | no | — |
| 254 | #41 | — | 284 | 8 | no | — |
| 255 | #41 | — | 142 | 2 | no | — |
| 256 | #41 | — | 142 | 2 | no | — |
| 257 | C2×Q8 | — | 284 | 2 | no | — |
| 258 | C2×Q8 | — | 284 | 2 | no | — |
| 259 | C2×Q8 | — | 284 | 4 | no | — |
| 260 | C2×Q8 | — | 284 | 4 | no | — |
| 261 | C2×Q8 | — | 284 | 8 | no | — |
| 262 | C2×Q8 | — | 71 | 1 | no | — |
| 263 | C2×Q8 | — | 142 | 4 | no | — |
| 264 | C2×Q8 | — | 142 | 2 | no | — |
| 265 | C2×Q8 | — | 142 | 2 | no | — |
| 266 | C2×Q8 | (C2×D71)⋊C4 | 1 | 2 | yes | — |
| 267 | C2×D4 | — | 2 | 2 | no | — |
| 268 | C2×D4 | — | 2 | 2 | no | — |
| 269 | C2×D4 | — | 71 | 1 | no | — |
| 270 | C2×D4 | — | 142 | 4 | no | — |
| 271 | C2×D4 | — | 142 | 1 | no | — |
| 272 | C2×D4 | (C2×D71)⋊C4 | 1 | 2 | yes | — |
| 273 | C22×C4 | — | 2 | 2 | no | — |
| 274 | C22×C4 | — | 71 | 4 | no | — |
| 275 | C22×C4 | — | 142 | 4 | no | — |
| 276 | C22×C4 | — | 142 | 4 | no | — |
| 277 | C22×C4 | — | 142 | 2 | no | — |
| 278 | C22×C4 | — | 142 | 1 | no | — |
| 279 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 280 | C22×C4 | D4×D71 | 1 | 2 | yes | — |
| 281 | M16 | — | 4 | 4 | no | — |
| 282 | M16 | — | 284 | 2 | no | — |
| 283 | M16 | — | 142 | 4 | no | — |
| 284 | C2×C8 | — | 4 | 2 | no | — |
| 285 | C2×C8 | — | 284 | 2 | no | — |
| 286 | C4⋊C4 | — | 2 | 2 | no | — |
| 287 | C4⋊C4 | — | 71 | 2 | no | — |
| 288 | C4⋊C4 | — | 142 | 8 | no | — |
| 289 | C4⋊C4 | — | 142 | 4 | no | — |
| 290 | C4⋊C4 | — | 142 | 2 | no | — |
| 291 | C4⋊C4 | — | 142 | 4 | no | — |
| 292 | C22⋊C4 | — | 2 | 4 | no | — |
| 293 | C22⋊C4 | — | 142 | 8 | no | — |
| 294 | C22⋊C4 | — | 142 | 1 | no | — |
| 295 | C22⋊C4 | — | 142 | 2 | no | — |
| 296 | C42 | — | 142 | 1 | no | — |
| 297 | C42 | — | 142 | 2 | no | — |
| 298 | C42 | D4×D71 | 1 | 2 | yes | — |
| 299 | C42 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 300 | C42 | C2×D284 | 1 | 1 | yes | characteristic |
| 301 | C23 | — | 2 | 2 | no | — |
| 302 | C23 | — | 142 | 1 | no | — |
| 303 | C23 | C22⋊C4×D71 | 1 | 1 | yes | characteristic |
| 304 | Q8 | — | 4 | 2 | no | — |
| 305 | Q8 | — | 284 | 4 | no | — |
| 306 | Q8 | — | 284 | 8 | no | — |
| 307 | Q8 | — | 284 | 2 | no | — |
| 308 | Q8 | — | 284 | 2 | no | — |
| 309 | Q8 | — | 71 | 2 | no | — |
| 310 | Q8 | — | 142 | 1 | no | — |
| 311 | D4 | — | 4 | 2 | no | — |
| 312 | D4 | — | 4 | 4 | no | — |
| 313 | D4 | — | 4 | 2 | no | — |
| 314 | D4 | — | 4 | 2 | no | — |
| 315 | D4 | — | 284 | 8 | no | — |
| 316 | D4 | — | 71 | 2 | no | — |
| 317 | D4 | — | 142 | 4 | no | — |
| 318 | D4 | — | 142 | 1 | no | — |
| 319 | C2×C4 | — | 2 | 2 | no | — |
| 320 | C2×C4 | — | 2 | 2 | no | — |
| 321 | C2×C4 | — | 2 | 1 | no | — |
| 322 | C2×C4 | — | 2 | 1 | no | — |
| 323 | C2×C4 | — | 2 | 2 | no | — |
| 324 | C2×C4 | — | 4 | 2 | no | — |
| 325 | C2×C4 | — | 4 | 2 | no | — |
| 326 | C2×C4 | — | 284 | 8 | no | — |
| 327 | C2×C4 | — | 284 | 8 | no | — |
| 328 | C2×C4 | — | 284 | 2 | no | — |
| 329 | C2×C4 | — | 284 | 2 | no | — |
| 330 | C2×C4 | — | 284 | 4 | no | — |
| 331 | C2×C4 | — | 142 | 4 | no | — |
| 332 | C2×C4 | — | 142 | 2 | no | — |
| 333 | C2×C4 | — | 142 | 4 | no | — |
| 334 | C2×C4 | — | 142 | 1 | no | — |
| 335 | C2×C4 | C22⋊C4×D71 | 1 | 1 | yes | characteristic |
| 336 | C2×C4 | C2×(C2×D71)⋊C4 | 1 | 1 | yes | characteristic |
| 337 | C2×C4 | #14556096 | 1 | 2 | yes | — |
| 338 | C2×C4 | #14556098 | 1 | 2 | yes | — |
| 339 | C8 | — | 8 | 2 | no | — |
| 340 | C8 | — | 284 | 4 | no | — |
| 341 | C22 | — | 2 | 1 | no | — |
| 342 | C22 | — | 2 | 2 | no | — |
| 343 | C22 | — | 4 | 2 | no | — |
| 344 | C22 | — | 4 | 4 | no | — |
| 345 | C22 | — | 284 | 2 | no | — |
| 346 | C22 | — | 142 | 2 | no | — |
| 347 | C22 | #17985854 | 1 | 1 | yes | characteristic |
| 348 | C4 | — | 2 | 1 | no | — |
| 349 | C4 | — | 2 | 2 | no | — |
| 350 | C4 | — | 4 | 2 | no | — |
| 351 | C4 | — | 284 | 4 | no | — |
| 352 | C4 | — | 284 | 2 | no | — |
| 353 | C4 | — | 142 | 2 | no | — |
| 354 | C4 | #100×D71 | 1 | 1 | yes | characteristic |
| 355 | C4 | #100×D71 | 1 | 1 | yes | characteristic |
| 356 | C4 | #17986170 | 1 | 2 | yes | — |
| 357 | C4 | #17986180 | 1 | 2 | yes | — |
| 358 | C2 | — | 4 | 1 | no | — |
| 359 | C2 | — | 8 | 2 | no | — |
| 360 | C2 | — | 284 | 2 | no | — |
| 361 | C2 | #22588259 | 1 | 1 | yes | characteristic |
| 362 | C2 | #22588297 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22589328 | C2 | semidirect |
| 3. #22586932 | C2 | semidirect |
| 4. #22586777 | C2 | semidirect |
| 5. C71×#1560 | C2 | semidirect |
| 184. #1560 | D71 | semidirect |
| 187. C71 | #8471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602120 | 2 |
| #22589328 | 2 |
| #22586932 | 2 |
| #22586777 | 2 |
| C71×#1560 | 2 |
| #8471 | 71 |