Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
464 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 464 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 | #22566791 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22561366 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22559219 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22559148 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22558214 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22558140 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C67×#1345 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16864027 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#14524016 | — | 2 | 1 | no | — |
| 10 | #16863727 | — | 2 | 1 | no | — |
| 11 | #16863547 | — | 2 | 1 | no | — |
| 12 | #16863402 | — | 2 | 1 | no | — |
| 13 | #16863326 | C22 | 1 | 1 | yes | characteristic |
| 14 | #16863312 | — | 2 | 1 | no | — |
| 15 | #16863304 | — | 2 | 1 | no | — |
| 16 | #16863297 | C22 | 1 | 1 | yes | characteristic |
| 17 | #16863290 | — | 2 | 1 | no | — |
| 18 | #16863272 | — | 2 | 1 | no | — |
| 19 | #16863258 | — | 2 | 1 | no | — |
| 20 | #16863157 | — | 2 | 1 | no | — |
| 21 | #16863134 | — | 2 | 1 | no | — |
| 22 | #16863132 | — | 2 | 1 | no | — |
| 23 | #16863122 | C22 | 1 | 1 | yes | characteristic |
| 24 | #394×C67 | C22 | 1 | 1 | yes | characteristic |
| 25 | #343×C67 | C22 | 1 | 1 | yes | characteristic |
| 26 | #324×C67 | C22 | 1 | 1 | yes | characteristic |
| 27 | C22×D268 | D4 | 1 | 1 | yes | characteristic |
| 28 | C22×C22⋊D67 | — | 2 | 1 | no | — |
| 29 | C22×C22⋊D67 | — | 2 | 1 | no | — |
| 30 | C22×C4×D67 | — | 2 | 1 | no | — |
| 31 | C2×#11761616 | — | 4 | 1 | no | — |
| 32 | #14524042 | — | 4 | 1 | no | — |
| 33 | #14524034 | — | 4 | 1 | no | — |
| 34 | #14524022 | — | 2 | 1 | no | — |
| 35 | #14524022 | — | 2 | 1 | no | — |
| 36 | #14524016 | — | 4 | 2 | no | — |
| 37 | #14524016 | — | 4 | 2 | no | — |
| 38 | #14524002 | — | 2 | 1 | no | — |
| 39 | C2×C4⋊Dic67 | D4 | 1 | 1 | yes | characteristic |
| 40 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 41 | C2×C22⋊Dic67 | — | 2 | 1 | no | — |
| 42 | C2×C22⋊Dic67 | — | 2 | 1 | no | — |
| 43 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 44 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 45 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 46 | C2×C4×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 47 | #14523975 | — | 4 | 1 | no | — |
| 48 | #14523968 | — | 4 | 1 | no | — |
| 49 | #14523965 | — | 4 | 1 | no | — |
| 50 | #14523965 | — | 4 | 1 | no | — |
| 51 | #14523964 | — | 4 | 1 | no | — |
| 52 | C22⋊(C67⋊C8) | — | 2 | 1 | no | — |
| 53 | C67⋊#95 | — | 2 | 1 | no | — |
| 54 | C67⋊#95 | — | 2 | 1 | no | — |
| 55 | C67⋊#95 | — | 2 | 1 | no | — |
| 56 | C67⋊#95 | D4 | 1 | 1 | yes | characteristic |
| 57 | C22×D4×C67 | D4 | 1 | 1 | yes | characteristic |
| 58 | C2×M16×C67 | — | 2 | 1 | no | — |
| 59 | C2×C4⋊C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×C22⋊C4×C67 | — | 2 | 1 | no | — |
| 61 | C2×C22⋊C4×C67 | — | 2 | 1 | no | — |
| 62 | C22⋊C8×C67 | — | 2 | 1 | no | — |
| 63 | #95×C67 | D4 | 1 | 1 | yes | characteristic |
| 64 | C23×D67 | — | 2 | 1 | no | — |
| 65 | C2×Dic134 | — | 2 | 1 | no | — |
| 66 | C2×Dic134 | — | 2 | 1 | no | — |
| 67 | C2×D268 | — | 2 | 1 | no | — |
| 68 | C2×D268 | — | 4 | 1 | no | — |
| 69 | C2×D268 | — | 4 | 1 | no | — |
| 70 | C2×D268 | SD16 | 1 | 2 | yes | complemented |
| 71 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 72 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 73 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 74 | C2×C22⋊D67 | — | 8 | 1 | no | — |
| 75 | C2×C22⋊D67 | — | 8 | 1 | no | — |
| 76 | C2×C22⋊D67 | — | 8 | 1 | no | — |
| 77 | C22×Dic67 | — | 2 | 1 | no | — |
| 78 | C22×Dic67 | — | 2 | 1 | no | — |
| 79 | C22×Dic67 | — | 2 | 1 | no | — |
| 80 | C2×C4×D67 | — | 4 | 2 | no | — |
| 81 | C2×C4×D67 | — | 4 | 2 | no | — |
| 82 | C2×C4×D67 | — | 8 | 1 | no | — |
| 83 | #11761616 | — | 8 | 2 | no | — |
| 84 | C2×C67⋊C8 | — | 4 | 1 | no | — |
| 85 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 86 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 87 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 88 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 89 | C4⋊Dic67 | — | 4 | 1 | no | — |
| 90 | Dic67⋊C4 | — | 4 | 1 | no | — |
| 91 | Dic67⋊C4 | — | 4 | 1 | no | — |
| 92 | Dic67⋊C4 | — | 4 | 1 | no | — |
| 93 | Dic67⋊C4 | — | 4 | 1 | no | — |
| 94 | C22⋊Dic67 | — | 4 | 2 | no | — |
| 95 | C22⋊Dic67 | — | 4 | 1 | no | — |
| 96 | C22⋊Dic67 | — | 8 | 1 | no | — |
| 97 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 98 | (C2×D67)⋊C4 | — | 8 | 1 | no | — |
| 99 | (C2×D67)⋊C4 | — | 8 | 1 | no | — |
| 100 | C4×Dic67 | — | 4 | 1 | no | — |
| 101 | C4×Dic67 | — | 4 | 1 | no | — |
| 102 | C24×C67 | — | 2 | 1 | no | — |
| 103 | C2×D4×C67 | — | 4 | 1 | no | — |
| 104 | C2×D4×C67 | — | 8 | 1 | no | — |
| 105 | C22×C4×C67 | — | 2 | 1 | no | — |
| 106 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | M16×C67 | — | 4 | 1 | no | — |
| 110 | M16×C67 | — | 4 | 1 | no | — |
| 111 | C2×C8×C67 | — | 4 | 1 | no | — |
| 112 | C2×C8×C67 | — | 4 | 1 | no | — |
| 113 | C4⋊C4×C67 | — | 4 | 1 | no | — |
| 114 | C22⋊C4×C67 | — | 4 | 1 | no | — |
| 115 | C22⋊C4×C67 | — | 4 | 1 | no | — |
| 116 | C22⋊C4×C67 | — | 8 | 1 | no | — |
| 117 | C23×C67 | — | 4 | 1 | no | — |
| 118 | C23×C67 | — | 4 | 1 | no | — |
| 119 | C23×C67 | — | 4 | 1 | no | — |
| 120 | C23×C67 | — | 4 | 1 | no | — |
| 121 | C23×C67 | — | 4 | 1 | no | — |
| 122 | C23×C67 | — | 4 | 1 | no | — |
| 123 | C23×C67 | — | 4 | 1 | no | — |
| 124 | C23×C67 | #120 | 1 | 1 | yes | characteristic |
| 125 | C22×D67 | — | 2 | 2 | no | — |
| 126 | C22×D67 | — | 4 | 1 | no | — |
| 127 | C22×D67 | — | 4 | 1 | no | — |
| 128 | C22×D67 | — | 4 | 1 | no | — |
| 129 | C22×D67 | — | 4 | 1 | no | — |
| 130 | C22×D67 | — | 4 | 1 | no | — |
| 131 | C22×D67 | — | 4 | 1 | no | — |
| 132 | D4×C67 | — | 4 | 2 | no | — |
| 133 | D4×C67 | — | 8 | 1 | no | — |
| 134 | C2×C4×C67 | — | 2 | 1 | no | — |
| 135 | C2×C4×C67 | — | 2 | 1 | no | — |
| 136 | C2×C4×C67 | — | 2 | 1 | no | — |
| 137 | C2×C4×C67 | — | 2 | 1 | no | — |
| 138 | C2×C4×C67 | — | 4 | 1 | no | — |
| 139 | C2×C4×C67 | — | 4 | 1 | no | — |
| 140 | C2×C4×C67 | — | 4 | 1 | no | — |
| 141 | C2×C4×C67 | — | 4 | 1 | no | — |
| 142 | C2×C4×C67 | — | 4 | 1 | no | — |
| 143 | C2×C4×C67 | C2×SD16 | 1 | 1 | yes | characteristic |
| 144 | C2×C4×C67 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 145 | C22⋊D67 | — | 8 | 4 | no | — |
| 146 | C22⋊D67 | — | 8 | 4 | no | — |
| 147 | C2×Dic67 | — | 2 | 2 | no | — |
| 148 | C2×Dic67 | — | 4 | 1 | no | — |
| 149 | C2×Dic67 | — | 4 | 1 | no | — |
| 150 | C2×Dic67 | — | 4 | 1 | no | — |
| 151 | C2×Dic67 | — | 4 | 1 | no | — |
| 152 | C2×Dic67 | — | 4 | 1 | no | — |
| 153 | C2×Dic67 | — | 4 | 1 | no | — |
| 154 | C2×Dic67 | — | 4 | 1 | no | — |
| 155 | C2×Dic67 | — | 4 | 1 | no | — |
| 156 | C2×Dic67 | — | 4 | 1 | no | — |
| 157 | C2×Dic67 | — | 4 | 1 | no | — |
| 158 | D268 | — | 4 | 2 | no | — |
| 159 | D268 | — | 8 | 1 | no | — |
| 160 | C4×D67 | — | 8 | 4 | no | — |
| 161 | Dic134 | — | 8 | 1 | no | — |
| 162 | Dic134 | — | 8 | 1 | no | — |
| 163 | C8×C67 | — | 8 | 1 | no | — |
| 164 | C8×C67 | — | 8 | 1 | no | — |
| 165 | C67⋊C8 | — | 8 | 1 | no | — |
| 166 | C22×C67 | — | 2 | 1 | no | — |
| 167 | C22×C67 | — | 2 | 1 | no | — |
| 168 | C22×C67 | — | 8 | 1 | no | — |
| 169 | C22×C67 | — | 8 | 1 | no | — |
| 170 | C22×C67 | — | 8 | 1 | no | — |
| 171 | C22×C67 | — | 8 | 1 | no | — |
| 172 | C22×C67 | — | 8 | 1 | no | — |
| 173 | C22×C67 | — | 8 | 1 | no | — |
| 174 | C22×C67 | — | 8 | 1 | no | — |
| 175 | C22×C67 | #450 | 1 | 1 | yes | characteristic |
| 176 | C22×C67 | #455 | 1 | 1 | yes | characteristic |
| 177 | C22×C67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 178 | C2×D67 | — | 4 | 2 | no | — |
| 179 | C2×D67 | — | 4 | 2 | no | — |
| 180 | C2×D67 | — | 4 | 2 | no | — |
| 181 | C2×D67 | — | 8 | 1 | no | — |
| 182 | C2×D67 | — | 8 | 1 | no | — |
| 183 | C2×D67 | — | 8 | 1 | no | — |
| 184 | C2×D67 | — | 8 | 1 | no | — |
| 185 | C4×C67 | — | 2 | 1 | no | — |
| 186 | C4×C67 | — | 2 | 1 | no | — |
| 187 | C4×C67 | — | 4 | 1 | no | — |
| 188 | C4×C67 | — | 4 | 1 | no | — |
| 189 | C4×C67 | — | 8 | 1 | no | — |
| 190 | Dic67 | — | 4 | 2 | no | — |
| 191 | Dic67 | — | 8 | 1 | no | — |
| 192 | Dic67 | — | 8 | 1 | no | — |
| 193 | Dic67 | — | 8 | 1 | no | — |
| 194 | Dic67 | — | 8 | 1 | no | — |
| 195 | #12211 | — | 67 | 1 | no | maximal, Sylow |
| 196 | C2×C67 | — | 2 | 1 | no | — |
| 197 | C2×C67 | — | 2 | 1 | no | — |
| 198 | C2×C67 | — | 16 | 1 | no | — |
| 199 | C2×C67 | #1601 | 1 | 1 | yes | characteristic |
| 200 | C2×C67 | #2200 | 1 | 1 | yes | characteristic |
| 201 | C2×C67 | #2204 | 1 | 1 | yes | characteristic |
| 202 | D67 | — | 8 | 2 | no | — |
| 203 | #2699 | — | 67 | 1 | no | — |
| 204 | #2027 | — | 67 | 1 | no | — |
| 205 | #1611 | — | 67 | 1 | no | — |
| 206 | #1599 | — | 67 | 1 | no | — |
| 207 | #1346 | — | 67 | 1 | no | — |
| 208 | #1345 | D67 | 1 | 1 | yes | characteristic, complemented |
| 209 | #1318 | — | 67 | 1 | no | — |
| 210 | C67 | #12211 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 211 | #544 | — | 67 | 1 | no | — |
| 212 | C2×#121 | — | 134 | 1 | no | — |
| 213 | #483 | — | 134 | 1 | no | — |
| 214 | #450 | — | 134 | 1 | no | — |
| 215 | #418 | — | 134 | 1 | no | — |
| 216 | #398 | — | 67 | 1 | no | — |
| 217 | #394 | — | 134 | 1 | no | — |
| 218 | #394 | C2×D67 | 1 | 1 | yes | characteristic |
| 219 | #392 | — | 134 | 1 | no | — |
| 220 | #390 | — | 67 | 1 | no | — |
| 221 | #388 | — | 134 | 1 | no | — |
| 222 | #386 | — | 134 | 1 | no | — |
| 223 | #381 | — | 134 | 1 | no | — |
| 224 | #343 | C2×D67 | 1 | 1 | yes | characteristic |
| 225 | #339 | — | 134 | 1 | no | — |
| 226 | #328 | — | 134 | 1 | no | — |
| 227 | #328 | — | 134 | 1 | no | — |
| 228 | #324 | — | 67 | 1 | no | — |
| 229 | #324 | C2×D67 | 1 | 1 | yes | characteristic |
| 230 | C22×D4 | — | 67 | 1 | no | — |
| 231 | C22×D4 | — | 134 | 1 | no | — |
| 232 | C22×D4 | — | 134 | 1 | no | — |
| 233 | C22×D4 | D268 | 1 | 1 | yes | characteristic |
| 234 | C23×C4 | — | 134 | 1 | no | — |
| 235 | C2×SD16 | — | 268 | 1 | no | — |
| 236 | C2×M16 | — | 2 | 1 | no | — |
| 237 | C4⋊Q8 | — | 268 | 1 | no | — |
| 238 | #125 | — | 268 | 1 | no | — |
| 239 | C22⋊Q8 | — | 134 | 1 | no | — |
| 240 | C22⋊Q8 | — | 134 | 1 | no | — |
| 241 | #121 | — | 268 | 2 | no | — |
| 242 | #121 | — | 268 | 2 | no | — |
| 243 | #117 | — | 134 | 1 | no | — |
| 244 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 245 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 246 | C2×C4⋊C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 247 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 248 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 249 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 250 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 251 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 252 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 253 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 254 | C2×C42 | — | 67 | 1 | no | — |
| 255 | #106 | — | 268 | 1 | no | — |
| 256 | #103 | — | 268 | 1 | no | — |
| 257 | #102 | — | 268 | 1 | no | — |
| 258 | #102 | — | 268 | 1 | no | — |
| 259 | #102 | — | 268 | 1 | no | — |
| 260 | C22⋊C8 | — | 2 | 1 | no | — |
| 261 | C22⋊C8 | — | 134 | 1 | no | — |
| 262 | #95 | — | 67 | 1 | no | — |
| 263 | #95 | — | 134 | 1 | no | — |
| 264 | #95 | — | 134 | 1 | no | — |
| 265 | #95 | — | 134 | 1 | no | — |
| 266 | #95 | D268 | 1 | 1 | yes | characteristic |
| 267 | C24 | — | 2 | 1 | no | — |
| 268 | C24 | — | 134 | 1 | no | — |
| 269 | C2×Q8 | — | 134 | 1 | no | — |
| 270 | C2×Q8 | — | 134 | 1 | no | — |
| 271 | C2×D4 | — | 4 | 1 | no | — |
| 272 | C2×D4 | — | 8 | 1 | no | — |
| 273 | C2×D4 | — | 268 | 1 | no | — |
| 274 | C2×D4 | — | 268 | 1 | no | — |
| 275 | C2×D4 | — | 268 | 2 | no | — |
| 276 | C2×D4 | — | 268 | 2 | no | — |
| 277 | C2×D4 | — | 268 | 2 | no | — |
| 278 | C2×D4 | — | 536 | 1 | no | — |
| 279 | C2×D4 | — | 536 | 1 | no | — |
| 280 | C2×D4 | — | 536 | 1 | no | — |
| 281 | C2×D4 | — | 67 | 2 | no | — |
| 282 | C2×D4 | — | 134 | 1 | no | — |
| 283 | C22×C4 | — | 2 | 1 | no | — |
| 284 | C22×C4 | — | 268 | 2 | no | — |
| 285 | C22×C4 | — | 268 | 2 | no | — |
| 286 | C22×C4 | — | 536 | 1 | no | — |
| 287 | C22×C4 | — | 134 | 1 | no | — |
| 288 | C22×C4 | — | 134 | 1 | no | — |
| 289 | C22×C4 | — | 134 | 1 | no | — |
| 290 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 291 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 292 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 293 | SD16 | — | 536 | 2 | no | — |
| 294 | M16 | — | 4 | 1 | no | — |
| 295 | M16 | — | 4 | 1 | no | — |
| 296 | C2×C8 | — | 4 | 1 | no | — |
| 297 | C2×C8 | — | 4 | 1 | no | — |
| 298 | C2×C8 | — | 268 | 1 | no | — |
| 299 | C4⋊C4 | — | 4 | 1 | no | — |
| 300 | C4⋊C4 | — | 268 | 1 | no | — |
| 301 | C4⋊C4 | — | 268 | 1 | no | — |
| 302 | C4⋊C4 | — | 268 | 1 | no | — |
| 303 | C4⋊C4 | — | 268 | 1 | no | — |
| 304 | C4⋊C4 | — | 268 | 1 | no | — |
| 305 | C4⋊C4 | — | 134 | 1 | no | — |
| 306 | C4⋊C4 | — | 134 | 1 | no | — |
| 307 | C4⋊C4 | — | 134 | 1 | no | — |
| 308 | C4⋊C4 | — | 134 | 1 | no | — |
| 309 | C22⋊C4 | — | 4 | 1 | no | — |
| 310 | C22⋊C4 | — | 4 | 1 | no | — |
| 311 | C22⋊C4 | — | 8 | 1 | no | — |
| 312 | C22⋊C4 | — | 268 | 2 | no | — |
| 313 | C22⋊C4 | — | 268 | 1 | no | — |
| 314 | C22⋊C4 | — | 268 | 2 | no | — |
| 315 | C22⋊C4 | — | 536 | 1 | no | — |
| 316 | C22⋊C4 | — | 536 | 1 | no | — |
| 317 | C22⋊C4 | — | 536 | 1 | no | — |
| 318 | C42 | — | 268 | 1 | no | — |
| 319 | C42 | — | 268 | 1 | no | — |
| 320 | C23 | — | 4 | 1 | no | — |
| 321 | C23 | — | 4 | 1 | no | — |
| 322 | C23 | — | 4 | 1 | no | — |
| 323 | C23 | — | 4 | 1 | no | — |
| 324 | C23 | — | 4 | 1 | no | — |
| 325 | C23 | — | 4 | 1 | no | — |
| 326 | C23 | — | 4 | 1 | no | — |
| 327 | C23 | — | 268 | 1 | no | — |
| 328 | C23 | — | 268 | 1 | no | — |
| 329 | C23 | — | 268 | 1 | no | — |
| 330 | C23 | — | 268 | 1 | no | — |
| 331 | C23 | — | 268 | 1 | no | — |
| 332 | C23 | — | 268 | 1 | no | — |
| 333 | C23 | — | 134 | 2 | no | — |
| 334 | C23 | #14524013 | 1 | 1 | yes | characteristic |
| 335 | Q8 | — | 536 | 1 | no | — |
| 336 | Q8 | — | 536 | 1 | no | — |
| 337 | D4 | — | 4 | 2 | no | — |
| 338 | D4 | — | 8 | 1 | no | — |
| 339 | D4 | — | 268 | 2 | no | — |
| 340 | D4 | — | 536 | 1 | no | — |
| 341 | D4 | — | 536 | 4 | no | — |
| 342 | D4 | — | 536 | 4 | no | — |
| 343 | C2×C4 | — | 2 | 1 | no | — |
| 344 | C2×C4 | — | 2 | 1 | no | — |
| 345 | C2×C4 | — | 2 | 1 | no | — |
| 346 | C2×C4 | — | 2 | 1 | no | — |
| 347 | C2×C4 | — | 4 | 1 | no | — |
| 348 | C2×C4 | — | 4 | 1 | no | — |
| 349 | C2×C4 | — | 4 | 1 | no | — |
| 350 | C2×C4 | — | 4 | 1 | no | — |
| 351 | C2×C4 | — | 4 | 1 | no | — |
| 352 | C2×C4 | — | 268 | 1 | no | — |
| 353 | C2×C4 | — | 268 | 1 | no | — |
| 354 | C2×C4 | — | 268 | 1 | no | — |
| 355 | C2×C4 | — | 268 | 1 | no | — |
| 356 | C2×C4 | — | 268 | 1 | no | — |
| 357 | C2×C4 | — | 268 | 1 | no | — |
| 358 | C2×C4 | — | 268 | 1 | no | — |
| 359 | C2×C4 | — | 268 | 1 | no | — |
| 360 | C2×C4 | — | 268 | 1 | no | — |
| 361 | C2×C4 | — | 268 | 1 | no | — |
| 362 | C2×C4 | — | 536 | 4 | no | — |
| 363 | C2×C4 | — | 134 | 2 | no | — |
| 364 | C2×C4 | SD16×D67 | 1 | 1 | yes | characteristic |
| 365 | C2×C4 | #14524067 | 1 | 1 | yes | characteristic |
| 366 | C8 | — | 8 | 1 | no | — |
| 367 | C8 | — | 8 | 1 | no | — |
| 368 | C8 | — | 536 | 1 | no | — |
| 369 | C22 | — | 2 | 1 | no | — |
| 370 | C22 | — | 2 | 1 | no | — |
| 371 | C22 | — | 8 | 1 | no | — |
| 372 | C22 | — | 8 | 1 | no | — |
| 373 | C22 | — | 8 | 1 | no | — |
| 374 | C22 | — | 8 | 1 | no | — |
| 375 | C22 | — | 8 | 1 | no | — |
| 376 | C22 | — | 8 | 1 | no | — |
| 377 | C22 | — | 8 | 1 | no | — |
| 378 | C22 | — | 268 | 2 | no | — |
| 379 | C22 | — | 268 | 2 | no | — |
| 380 | C22 | — | 268 | 2 | no | — |
| 381 | C22 | — | 536 | 1 | no | — |
| 382 | C22 | — | 536 | 1 | no | — |
| 383 | C22 | — | 536 | 1 | no | — |
| 384 | C22 | — | 536 | 1 | no | — |
| 385 | C22 | #16863548 | 1 | 1 | yes | characteristic |
| 386 | C22 | #16863575 | 1 | 1 | yes | characteristic |
| 387 | C22 | #16863584 | 1 | 1 | yes | characteristic |
| 388 | C4 | — | 2 | 1 | no | — |
| 389 | C4 | — | 2 | 1 | no | — |
| 390 | C4 | — | 4 | 1 | no | — |
| 391 | C4 | — | 4 | 1 | no | — |
| 392 | C4 | — | 8 | 1 | no | — |
| 393 | C4 | — | 268 | 2 | no | — |
| 394 | C4 | — | 536 | 1 | no | — |
| 395 | C4 | — | 536 | 1 | no | — |
| 396 | C4 | — | 536 | 1 | no | — |
| 397 | C4 | — | 536 | 1 | no | — |
| 398 | C2 | — | 2 | 1 | no | — |
| 399 | C2 | — | 2 | 1 | no | — |
| 400 | C2 | — | 16 | 1 | no | — |
| 401 | C2 | — | 536 | 2 | no | — |
| 402 | C2 | #22559162 | 1 | 1 | yes | characteristic |
| 403 | C2 | #22562218 | 1 | 1 | yes | characteristic |
| 404 | C2 | #22562236 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22561366 | C2 | semidirect |
| 3. #22559219 | C2 | semidirect |
| 4. #22559148 | C2 | semidirect |
| 5. #22558214 | C2 | semidirect |
| 6. #22558140 | C2 | semidirect |
| 7. C67×#1345 | C2 | semidirect |
| 70. C2×D268 | SD16 | semidirect |
| 208. #1345 | D67 | semidirect |
| 210. C67 | #12211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22566791 | 2 |
| #22561366 | 2 |
| #22559219 | 2 |
| #22559148 | 2 |
| #22558214 | 2 |
| #22558140 | 2 |
| C67×#1345 | 2 |
| #12211 | 67 |