Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
580 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 80 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 | #22626796 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22625676 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22625328 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22624778 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22615824 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #17989621 | — | 2 | 4 | no | — |
| 7 | #17989603 | — | 2 | 1 | no | — |
| 8 | C2×#14556650 | — | 2 | 1 | no | — |
| 9 | #17989558 | — | 2 | 1 | no | — |
| 10 | #17989558 | C22 | 1 | 2 | yes | — |
| 11 | C4×C22⋊#64408 | C22 | 1 | 2 | yes | — |
| 12 | #17989465 | — | 2 | 1 | no | — |
| 13 | #17989439 | — | 2 | 4 | no | — |
| 14 | C2×#14556566 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#14556553 | C22 | 1 | 1 | yes | characteristic |
| 16 | #17988522 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #17988505 | — | 2 | 1 | no | — |
| 18 | #17988504 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #17988497 | — | 2 | 1 | no | — |
| 20 | #17988497 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | #17988476 | — | 2 | 1 | no | — |
| 22 | #17988465 | — | 2 | 1 | no | — |
| 23 | #17988449 | C22 | 1 | 1 | yes | characteristic |
| 24 | #400×C73 | C4 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#11924038 | — | 2 | 2 | no | — |
| 26 | C2×#11924038 | — | 2 | 2 | no | — |
| 27 | C2×C22⋊#64408 | — | 2 | 2 | no | — |
| 28 | C2×C4×#64408 | — | 2 | 2 | no | — |
| 29 | C4⋊#10596833 | — | 2 | 2 | no | — |
| 30 | #14556650 | — | 2 | 4 | no | — |
| 31 | #14556648 | — | 2 | 2 | no | — |
| 32 | #14556648 | D4 | 1 | 4 | yes | complemented |
| 33 | C22⋊#10596833 | — | 2 | 2 | no | — |
| 34 | C4×#10596833 | — | 2 | 2 | no | — |
| 35 | (C2×#64408)⋊C4 | — | 2 | 2 | no | — |
| 36 | C22×D292 | — | 2 | 1 | no | — |
| 37 | C22×D292 | — | 2 | 1 | no | — |
| 38 | C22×D292 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C22×D292 | D4 | 1 | 1 | yes | characteristic |
| 40 | C22×C4×D73 | D4 | 1 | 1 | yes | characteristic |
| 41 | C22×C4×D73 | C23 | 1 | 1 | yes | characteristic |
| 42 | #14556566 | — | 2 | 2 | no | — |
| 43 | #14556566 | — | 2 | 2 | no | — |
| 44 | #14556553 | — | 2 | 2 | no | — |
| 45 | #14556553 | — | 2 | 2 | no | — |
| 46 | C2×#11924007 | — | 2 | 1 | no | — |
| 47 | C2×#11924005 | — | 2 | 1 | no | — |
| 48 | C2×#11924005 | — | 2 | 1 | no | — |
| 49 | C2×#11924005 | — | 2 | 1 | no | — |
| 50 | C2×#11924005 | — | 2 | 1 | no | — |
| 51 | C2×#11924005 | — | 2 | 1 | no | — |
| 52 | C2×#11924005 | — | 2 | 1 | no | — |
| 53 | C2×#11924005 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C2×#11924005 | D4 | 1 | 1 | yes | characteristic |
| 55 | C2×C4×Dic73 | D4 | 1 | 1 | yes | characteristic |
| 56 | #14556498 | — | 2 | 1 | no | — |
| 57 | #14556498 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | C2×C4⋊C4×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | C2×C4⋊C4×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | #95×C73 | — | 2 | 1 | no | — |
| 61 | #95×C73 | — | 2 | 1 | no | — |
| 62 | #95×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | C22×#64408 | — | 4 | 2 | no | — |
| 64 | #11924038 | — | 8 | 2 | no | — |
| 65 | #11924038 | — | 8 | 2 | no | — |
| 66 | C2×#10596833 | — | 2 | 4 | no | — |
| 67 | C22⋊#64408 | — | 2 | 4 | no | — |
| 68 | C22⋊#64408 | — | 4 | 2 | no | — |
| 69 | C4×#64408 | — | 8 | 2 | no | — |
| 70 | C23×D73 | — | 2 | 1 | no | — |
| 71 | C23×D73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 72 | C23×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 73 | C2×D292 | — | 2 | 2 | no | — |
| 74 | C2×D292 | — | 2 | 2 | no | — |
| 75 | C2×D292 | — | 2 | 2 | no | — |
| 76 | C2×D292 | — | 4 | 1 | no | — |
| 77 | C2×D292 | — | 4 | 2 | no | — |
| 78 | C2×D292 | — | 4 | 2 | no | — |
| 79 | C2×D292 | — | 8 | 1 | no | — |
| 80 | C2×D292 | — | 8 | 1 | no | — |
| 81 | C2×D292 | — | 8 | 1 | no | — |
| 82 | C2×D292 | — | 8 | 1 | no | — |
| 83 | C2×D292 | — | 8 | 1 | no | — |
| 84 | C22×Dic73 | — | 2 | 1 | no | — |
| 85 | C22×Dic73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 86 | C22×Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C2×C4×D73 | — | 2 | 1 | no | — |
| 88 | C2×C4×D73 | — | 2 | 1 | no | — |
| 89 | C2×C4×D73 | — | 8 | 1 | no | — |
| 90 | C2×C4×D73 | — | 8 | 1 | no | — |
| 91 | C2×C4×D73 | C2×D4 | 1 | 2 | yes | — |
| 92 | C2×C4×D73 | #41 | 1 | 2 | yes | — |
| 93 | #11924007 | — | 8 | 1 | no | — |
| 94 | #11924005 | — | 2 | 2 | no | — |
| 95 | #11924005 | — | 2 | 2 | no | — |
| 96 | #11924005 | — | 4 | 2 | no | — |
| 97 | #11924005 | — | 4 | 1 | no | — |
| 98 | #11924005 | — | 4 | 1 | no | — |
| 99 | #11924005 | — | 8 | 1 | no | — |
| 100 | #11924005 | — | 8 | 1 | no | — |
| 101 | #11924005 | — | 8 | 1 | no | — |
| 102 | #11924005 | — | 8 | 1 | no | — |
| 103 | C4×Dic73 | — | 2 | 1 | no | — |
| 104 | C4×Dic73 | — | 2 | 1 | no | — |
| 105 | C22×C4×C73 | — | 2 | 1 | no | — |
| 106 | C22×C4×C73 | — | 2 | 1 | no | — |
| 107 | C22×C4×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 108 | C22×C4×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 109 | C22×C4×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 110 | C4⋊C4×C73 | — | 2 | 2 | no | — |
| 111 | C4⋊C4×C73 | — | 2 | 2 | no | — |
| 112 | C23×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 113 | C22×D73 | — | 2 | 1 | no | — |
| 114 | C22×D73 | — | 2 | 1 | no | — |
| 115 | C22×D73 | — | 2 | 1 | no | — |
| 116 | C22×D73 | — | 2 | 1 | no | — |
| 117 | C22×D73 | — | 2 | 1 | no | — |
| 118 | C22×D73 | — | 4 | 1 | no | — |
| 119 | C22×D73 | — | 4 | 1 | no | — |
| 120 | C22×D73 | — | 4 | 1 | no | — |
| 121 | C22×D73 | — | 4 | 1 | no | — |
| 122 | C22×D73 | — | 4 | 1 | no | — |
| 123 | C22×D73 | — | 4 | 1 | no | — |
| 124 | C22×D73 | — | 4 | 1 | no | — |
| 125 | C22×D73 | — | 4 | 1 | no | — |
| 126 | C22×D73 | — | 4 | 1 | no | — |
| 127 | C22×D73 | — | 4 | 1 | no | — |
| 128 | C22×D73 | — | 4 | 1 | no | — |
| 129 | C22×D73 | #121 | 1 | 2 | yes | — |
| 130 | C2×#64408 | — | 4 | 4 | no | — |
| 131 | C2×#64408 | — | 8 | 2 | no | — |
| 132 | C2×#64408 | — | 8 | 2 | no | — |
| 133 | C2×C4×C73 | — | 2 | 1 | no | — |
| 134 | C2×C4×C73 | — | 2 | 1 | no | — |
| 135 | C2×C4×C73 | — | 2 | 1 | no | — |
| 136 | C2×C4×C73 | — | 4 | 1 | no | — |
| 137 | C2×C4×C73 | — | 4 | 1 | no | — |
| 138 | C2×C4×C73 | — | 4 | 1 | no | — |
| 139 | C2×C4×C73 | — | 4 | 1 | no | — |
| 140 | C2×C4×C73 | — | 4 | 1 | no | — |
| 141 | C2×C4×C73 | — | 4 | 1 | no | — |
| 142 | C2×C4×C73 | — | 4 | 1 | no | — |
| 143 | C2×C4×C73 | — | 4 | 1 | no | — |
| 144 | C2×C4×C73 | #104 | 1 | 2 | yes | — |
| 145 | C2×C4×C73 | C4×D4 | 1 | 2 | yes | — |
| 146 | C2×Dic73 | — | 2 | 1 | no | — |
| 147 | C2×Dic73 | — | 4 | 1 | no | — |
| 148 | C2×Dic73 | — | 4 | 1 | no | — |
| 149 | C2×Dic73 | — | 4 | 1 | no | — |
| 150 | C2×Dic73 | — | 4 | 1 | no | — |
| 151 | C2×Dic73 | — | 4 | 1 | no | — |
| 152 | C2×Dic73 | #120 | 1 | 1 | yes | characteristic |
| 153 | C2×Dic73 | #123 | 1 | 1 | yes | characteristic |
| 154 | D292 | — | 4 | 4 | no | — |
| 155 | D292 | — | 8 | 2 | no | — |
| 156 | D292 | — | 8 | 4 | no | — |
| 157 | D292 | — | 8 | 4 | no | — |
| 158 | C4×D73 | — | 4 | 2 | no | — |
| 159 | C4×D73 | — | 4 | 2 | no | — |
| 160 | C4×D73 | — | 4 | 2 | no | — |
| 161 | C4×D73 | — | 8 | 1 | no | — |
| 162 | #10596833 | — | 4 | 4 | no | — |
| 163 | C22×C73 | — | 2 | 1 | no | — |
| 164 | C22×C73 | — | 2 | 1 | no | — |
| 165 | C22×C73 | #386 | 1 | 1 | yes | characteristic |
| 166 | C22×C73 | C2×#104 | 1 | 1 | yes | characteristic |
| 167 | C22×C73 | #421 | 1 | 1 | yes | characteristic |
| 168 | C2×D73 | — | 2 | 2 | no | — |
| 169 | C2×D73 | — | 2 | 2 | no | — |
| 170 | C2×D73 | — | 2 | 2 | no | — |
| 171 | C2×D73 | — | 4 | 2 | no | — |
| 172 | C2×D73 | — | 4 | 1 | no | — |
| 173 | C2×D73 | — | 4 | 1 | no | — |
| 174 | C2×D73 | — | 4 | 1 | no | — |
| 175 | C2×D73 | — | 8 | 1 | no | — |
| 176 | C2×D73 | — | 8 | 1 | no | — |
| 177 | C2×D73 | — | 8 | 1 | no | — |
| 178 | C2×D73 | — | 8 | 1 | no | — |
| 179 | C2×D73 | — | 8 | 1 | no | — |
| 180 | C2×D73 | — | 8 | 1 | no | — |
| 181 | C2×D73 | — | 8 | 1 | no | — |
| 182 | C2×D73 | — | 8 | 1 | no | — |
| 183 | C2×D73 | — | 8 | 1 | no | — |
| 184 | C2×D73 | — | 8 | 1 | no | — |
| 185 | #64408 | — | 8 | 4 | no | — |
| 186 | C4×C73 | — | 2 | 2 | no | — |
| 187 | C4×C73 | — | 2 | 2 | no | — |
| 188 | C4×C73 | — | 4 | 1 | no | — |
| 189 | C4×C73 | — | 8 | 1 | no | — |
| 190 | C4×C73 | — | 8 | 1 | no | — |
| 191 | Dic73 | — | 2 | 1 | no | — |
| 192 | Dic73 | — | 2 | 1 | no | — |
| 193 | Dic73 | — | 4 | 1 | no | — |
| 194 | Dic73 | — | 8 | 1 | no | — |
| 195 | #9186 | — | 73 | 1 | no | maximal, Sylow |
| 196 | C2×C73 | — | 2 | 1 | no | — |
| 197 | C2×C73 | — | 2 | 1 | no | — |
| 198 | C2×C73 | #1871 | 1 | 1 | yes | characteristic |
| 199 | C2×C73 | #1910 | 1 | 1 | yes | characteristic |
| 200 | C2×C73 | #1913 | 1 | 1 | yes | characteristic |
| 201 | D73 | — | 4 | 2 | no | — |
| 202 | D73 | — | 8 | 1 | no | — |
| 203 | D73 | — | 16 | 1 | no | — |
| 204 | #2975 | — | 73 | 1 | no | — |
| 205 | #2635 | — | 73 | 1 | no | — |
| 206 | C4×#99 | — | 73 | 1 | no | — |
| 207 | #1507 | — | 73 | 2 | no | — |
| 208 | #1284 | — | 73 | 2 | no | — |
| 209 | C73 | #9186 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 210 | C2×#121 | — | 73 | 1 | no | — |
| 211 | C2×C4×D4 | — | 73 | 1 | no | — |
| 212 | #436 | — | 146 | 4 | no | — |
| 213 | #431 | — | 146 | 1 | no | — |
| 214 | C2×#99 | — | 146 | 1 | no | — |
| 215 | #407 | — | 73 | 2 | no | — |
| 216 | #407 | — | 146 | 1 | no | — |
| 217 | #400 | #64408 | 1 | 1 | yes | characteristic, complemented |
| 218 | #399 | — | 73 | 1 | no | — |
| 219 | #394 | — | 73 | 1 | no | — |
| 220 | #394 | — | 146 | 1 | no | — |
| 221 | #392 | — | 73 | 1 | no | — |
| 222 | #392 | — | 146 | 1 | no | — |
| 223 | #388 | — | 146 | 1 | no | — |
| 224 | #386 | — | 146 | 1 | no | — |
| 225 | #381 | — | 73 | 1 | no | — |
| 226 | C4×C22⋊C4 | — | 73 | 2 | no | — |
| 227 | #342 | — | 146 | 1 | no | — |
| 228 | #327 | — | 146 | 4 | no | — |
| 229 | C22×D4 | — | 73 | 1 | no | — |
| 230 | C22×D4 | — | 73 | 1 | no | — |
| 231 | C22×D4 | — | 146 | 1 | no | — |
| 232 | C22×D4 | — | 146 | 1 | no | — |
| 233 | C23×C4 | — | 73 | 1 | no | — |
| 234 | C23×C4 | — | 73 | 1 | no | — |
| 235 | C2×M16 | — | 146 | 2 | no | — |
| 236 | C2×M16 | — | 146 | 2 | no | — |
| 237 | #121 | — | 146 | 2 | no | — |
| 238 | #121 | — | 146 | 2 | no | — |
| 239 | C4×D4 | — | 146 | 2 | no | — |
| 240 | C4×D4 | — | 146 | 2 | no | — |
| 241 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 242 | C2×C4⋊C4 | C2×#64408 | 1 | 1 | yes | characteristic |
| 243 | C2×C4⋊C4 | C2×#64408 | 1 | 1 | yes | characteristic |
| 244 | C2×C22⋊C4 | — | 73 | 1 | no | — |
| 245 | C2×C22⋊C4 | — | 73 | 1 | no | — |
| 246 | C2×C22⋊C4 | — | 146 | 1 | no | — |
| 247 | C2×C22⋊C4 | — | 146 | 1 | no | — |
| 248 | C2×C22⋊C4 | — | 146 | 2 | no | — |
| 249 | C2×C22⋊C4 | — | 146 | 1 | no | — |
| 250 | C2×C22⋊C4 | — | 146 | 1 | no | — |
| 251 | C2×C22⋊C4 | — | 146 | 1 | no | — |
| 252 | C2×C22⋊C4 | — | 146 | 1 | no | — |
| 253 | C2×C42 | — | 73 | 1 | no | — |
| 254 | C2×C42 | — | 146 | 2 | no | — |
| 255 | C4⋊C8 | — | 146 | 2 | no | — |
| 256 | #99 | — | 146 | 4 | no | — |
| 257 | C22⋊C8 | — | 73 | 4 | no | — |
| 258 | C22⋊C8 | — | 146 | 2 | no | — |
| 259 | C22⋊C8 | — | 146 | 2 | no | — |
| 260 | C4×C8 | — | 146 | 2 | no | — |
| 261 | #95 | — | 2 | 1 | no | — |
| 262 | #95 | — | 2 | 1 | no | — |
| 263 | #95 | — | 73 | 1 | no | — |
| 264 | #95 | — | 146 | 1 | no | — |
| 265 | #95 | — | 146 | 2 | no | — |
| 266 | #95 | C2×#64408 | 1 | 1 | yes | characteristic |
| 267 | C24 | — | 73 | 1 | no | — |
| 268 | C24 | — | 73 | 1 | no | — |
| 269 | C24 | — | 146 | 1 | no | — |
| 270 | C2×D4 | — | 292 | 1 | no | — |
| 271 | C2×D4 | — | 292 | 2 | no | — |
| 272 | C2×D4 | — | 292 | 2 | no | — |
| 273 | C2×D4 | — | 584 | 1 | no | — |
| 274 | C2×D4 | — | 584 | 1 | no | — |
| 275 | C2×D4 | — | 584 | 1 | no | — |
| 276 | C2×D4 | — | 584 | 1 | no | — |
| 277 | C2×D4 | — | 584 | 1 | no | — |
| 278 | C2×D4 | — | 146 | 2 | no | — |
| 279 | C2×D4 | — | 146 | 2 | no | — |
| 280 | C2×D4 | — | 146 | 2 | no | — |
| 281 | C22×C4 | — | 2 | 1 | no | — |
| 282 | C22×C4 | — | 2 | 1 | no | — |
| 283 | C22×C4 | — | 292 | 2 | no | — |
| 284 | C22×C4 | — | 584 | 1 | no | — |
| 285 | C22×C4 | — | 584 | 1 | no | — |
| 286 | C22×C4 | — | 73 | 1 | no | — |
| 287 | C22×C4 | — | 73 | 2 | no | — |
| 288 | C22×C4 | — | 73 | 2 | no | — |
| 289 | C22×C4 | — | 73 | 1 | no | — |
| 290 | C22×C4 | — | 146 | 1 | no | — |
| 291 | C22×C4 | — | 146 | 1 | no | — |
| 292 | C22×C4 | — | 146 | 1 | no | — |
| 293 | C22×C4 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 294 | C22×C4 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 295 | C22×C4 | C22×#64408 | 1 | 1 | yes | characteristic |
| 296 | M16 | — | 584 | 2 | no | — |
| 297 | M16 | — | 584 | 2 | no | — |
| 298 | C2×C8 | — | 146 | 4 | no | — |
| 299 | C4⋊C4 | — | 2 | 2 | no | — |
| 300 | C4⋊C4 | — | 2 | 2 | no | — |
| 301 | C4⋊C4 | — | 584 | 1 | no | — |
| 302 | C22⋊C4 | — | 292 | 1 | no | — |
| 303 | C22⋊C4 | — | 292 | 1 | no | — |
| 304 | C22⋊C4 | — | 292 | 2 | no | — |
| 305 | C22⋊C4 | — | 292 | 2 | no | — |
| 306 | C22⋊C4 | — | 584 | 1 | no | — |
| 307 | C22⋊C4 | — | 584 | 1 | no | — |
| 308 | C22⋊C4 | — | 584 | 1 | no | — |
| 309 | C22⋊C4 | — | 584 | 1 | no | — |
| 310 | C22⋊C4 | — | 146 | 2 | no | — |
| 311 | C22⋊C4 | — | 146 | 4 | no | — |
| 312 | C22⋊C4 | — | 146 | 2 | no | — |
| 313 | C42 | — | 584 | 2 | no | — |
| 314 | C42 | — | 146 | 1 | no | — |
| 315 | C42 | — | 146 | 1 | no | — |
| 316 | C23 | — | 292 | 1 | no | — |
| 317 | C23 | — | 292 | 1 | no | — |
| 318 | C23 | — | 292 | 1 | no | — |
| 319 | C23 | — | 292 | 1 | no | — |
| 320 | C23 | — | 292 | 1 | no | — |
| 321 | C23 | — | 292 | 1 | no | — |
| 322 | C23 | — | 292 | 1 | no | — |
| 323 | C23 | — | 292 | 1 | no | — |
| 324 | C23 | — | 292 | 1 | no | — |
| 325 | C23 | — | 292 | 1 | no | — |
| 326 | C23 | — | 292 | 1 | no | — |
| 327 | C23 | — | 73 | 2 | no | — |
| 328 | C23 | — | 146 | 1 | no | — |
| 329 | C23 | — | 146 | 1 | no | — |
| 330 | C23 | — | 146 | 1 | no | — |
| 331 | C23 | — | 146 | 1 | no | — |
| 332 | C23 | — | 146 | 1 | no | — |
| 333 | C23 | C2×C22⋊#64408 | 1 | 1 | yes | characteristic |
| 334 | D4 | — | 292 | 4 | no | — |
| 335 | D4 | — | 584 | 2 | no | — |
| 336 | D4 | — | 584 | 4 | no | — |
| 337 | D4 | — | 584 | 4 | no | — |
| 338 | C2×C4 | — | 2 | 1 | no | — |
| 339 | C2×C4 | — | 2 | 1 | no | — |
| 340 | C2×C4 | — | 2 | 1 | no | — |
| 341 | C2×C4 | — | 4 | 1 | no | — |
| 342 | C2×C4 | — | 4 | 1 | no | — |
| 343 | C2×C4 | — | 4 | 1 | no | — |
| 344 | C2×C4 | — | 4 | 1 | no | — |
| 345 | C2×C4 | — | 4 | 1 | no | — |
| 346 | C2×C4 | — | 4 | 1 | no | — |
| 347 | C2×C4 | — | 4 | 1 | no | — |
| 348 | C2×C4 | — | 4 | 1 | no | — |
| 349 | C2×C4 | — | 292 | 2 | no | — |
| 350 | C2×C4 | — | 292 | 2 | no | — |
| 351 | C2×C4 | — | 292 | 2 | no | — |
| 352 | C2×C4 | — | 292 | 1 | no | — |
| 353 | C2×C4 | — | 292 | 1 | no | — |
| 354 | C2×C4 | — | 292 | 1 | no | — |
| 355 | C2×C4 | — | 292 | 4 | no | — |
| 356 | C2×C4 | — | 292 | 1 | no | — |
| 357 | C2×C4 | — | 292 | 1 | no | — |
| 358 | C2×C4 | — | 584 | 1 | no | — |
| 359 | C2×C4 | — | 584 | 2 | no | — |
| 360 | C2×C4 | — | 584 | 2 | no | — |
| 361 | C2×C4 | — | 73 | 1 | no | — |
| 362 | C2×C4 | — | 73 | 1 | no | — |
| 363 | C2×C4 | — | 146 | 1 | no | — |
| 364 | C2×C4 | #14556656 | 1 | 2 | yes | — |
| 365 | C2×C4 | D4×#64408 | 1 | 2 | yes | — |
| 366 | C8 | — | 292 | 4 | no | — |
| 367 | C22 | — | 2 | 1 | no | — |
| 368 | C22 | — | 2 | 1 | no | — |
| 369 | C22 | — | 292 | 2 | no | — |
| 370 | C22 | — | 292 | 1 | no | — |
| 371 | C22 | — | 292 | 1 | no | — |
| 372 | C22 | — | 292 | 1 | no | — |
| 373 | C22 | — | 584 | 1 | no | — |
| 374 | C22 | — | 584 | 1 | no | — |
| 375 | C22 | — | 584 | 1 | no | — |
| 376 | C22 | — | 584 | 1 | no | — |
| 377 | C22 | — | 584 | 1 | no | — |
| 378 | C22 | — | 584 | 1 | no | — |
| 379 | C22 | — | 584 | 1 | no | — |
| 380 | C22 | — | 584 | 1 | no | — |
| 381 | C22 | — | 584 | 1 | no | — |
| 382 | C22 | — | 584 | 1 | no | — |
| 383 | C22 | — | 146 | 2 | no | — |
| 384 | C22 | — | 146 | 2 | no | — |
| 385 | C22 | — | 146 | 2 | no | — |
| 386 | C22 | #17989535 | 1 | 1 | yes | characteristic |
| 387 | C22 | C2×#14556656 | 1 | 1 | yes | characteristic |
| 388 | C22 | #17989584 | 1 | 1 | yes | characteristic |
| 389 | C4 | — | 2 | 2 | no | — |
| 390 | C4 | — | 2 | 2 | no | — |
| 391 | C4 | — | 4 | 1 | no | — |
| 392 | C4 | — | 8 | 1 | no | — |
| 393 | C4 | — | 8 | 1 | no | — |
| 394 | C4 | — | 292 | 1 | no | — |
| 395 | C4 | — | 584 | 1 | no | — |
| 396 | C4 | — | 584 | 4 | no | — |
| 397 | C4 | — | 146 | 1 | no | — |
| 398 | C4 | — | 146 | 1 | no | — |
| 399 | C2 | — | 2 | 1 | no | — |
| 400 | C2 | — | 2 | 1 | no | — |
| 401 | C2 | — | 292 | 2 | no | — |
| 402 | C2 | — | 584 | 1 | no | — |
| 403 | C2 | — | 1168 | 1 | no | — |
| 404 | C2 | #22625912 | 1 | 1 | yes | characteristic |
| 405 | C2 | #22625975 | 1 | 1 | yes | characteristic |
| 406 | C2 | #22625981 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626796 | C2 | semidirect |
| 2. #22625676 | C2 | semidirect |
| 3. #22625328 | C2 | semidirect |
| 4. #22624778 | C2 | semidirect |
| 16. #17988522 | C4 | semidirect |
| 18. #17988504 | C4 | semidirect |
| 20. #17988497 | C4 | semidirect |
| 24. #400×C73 | C4 | semidirect |
| 32. #14556648 | D4 | semidirect |
| 209. C73 | #9186 | semidirect |
| 217. #400 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626796 | 2 |
| #22625676 | 2 |
| #22625328 | 2 |
| #22624778 | 2 |
| #22615824 | 2 |
| #9186 | 73 |