Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
716 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 135 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 | #22572801 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22571805 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22559795 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22559710 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22559673 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22559495 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22559290 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22559091 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C67×#1629 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#14524069 | — | 2 | 2 | no | — |
| 11 | #16864112 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #16864051 | C22 | 1 | 2 | yes | — |
| 13 | #16863794 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #16863792 | C22 | 1 | 2 | yes | complemented |
| 15 | #16863768 | C22 | 1 | 2 | yes | — |
| 16 | #16863718 | — | 2 | 2 | no | — |
| 17 | #16863716 | — | 2 | 2 | no | — |
| 18 | #16863677 | C22 | 1 | 2 | yes | complemented |
| 19 | #16863648 | — | 2 | 2 | no | — |
| 20 | #16863640 | — | 2 | 2 | no | — |
| 21 | #16863601 | C22 | 1 | 2 | yes | — |
| 22 | #16863588 | C22 | 1 | 2 | yes | — |
| 23 | #16863547 | — | 2 | 2 | no | — |
| 24 | #16863539 | — | 2 | 2 | no | — |
| 25 | C4×#11761613 | C22 | 1 | 2 | yes | — |
| 26 | #16863474 | C22 | 1 | 2 | yes | — |
| 27 | #16863473 | C22 | 1 | 2 | yes | complemented |
| 28 | #16863435 | — | 2 | 2 | no | — |
| 29 | #16863148 | C22 | 1 | 2 | yes | complemented |
| 30 | #16863145 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #16863143 | C22 | 1 | 2 | yes | complemented |
| 32 | #16863125 | C22 | 1 | 2 | yes | complemented |
| 33 | C8×C67⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | D42×C67 | C22 | 1 | 1 | yes | characteristic |
| 35 | #492×C67 | C22 | 1 | 1 | yes | characteristic |
| 36 | #476×C67 | C22 | 1 | 2 | yes | — |
| 37 | #331×C67 | C22 | 1 | 1 | yes | characteristic |
| 38 | D4⋊C8×C67 | C22 | 1 | 2 | yes | — |
| 39 | C2×#11761628 | — | 2 | 2 | no | — |
| 40 | #14524069 | — | 4 | 8 | no | — |
| 41 | C2×#11761616 | — | 2 | 2 | no | — |
| 42 | C2×#11761616 | — | 2 | 2 | no | — |
| 43 | C2×#11761616 | — | 2 | 2 | no | — |
| 44 | C2×#11761613 | — | 2 | 2 | no | — |
| 45 | C2×#11761613 | D4 | 1 | 2 | yes | — |
| 46 | C2×#11761612 | — | 2 | 2 | no | — |
| 47 | C2×#11761611 | — | 2 | 2 | no | — |
| 48 | #14524043 | C23 | 1 | 2 | yes | — |
| 49 | #14524032 | — | 4 | 1 | no | — |
| 50 | #14524025 | — | 4 | 2 | no | — |
| 51 | #14524022 | — | 2 | 2 | no | — |
| 52 | #14524018 | — | 2 | 2 | no | — |
| 53 | #14524014 | — | 2 | 2 | no | — |
| 54 | C4×D268 | C23 | 1 | 2 | yes | — |
| 55 | #14524001 | — | 2 | 2 | no | — |
| 56 | C4⋊C4×D67 | — | 2 | 2 | no | — |
| 57 | #14523977 | — | 2 | 2 | no | — |
| 58 | #14523976 | D4 | 1 | 2 | yes | — |
| 59 | #14523975 | — | 4 | 1 | no | — |
| 60 | #14523974 | — | 2 | 2 | no | — |
| 61 | #14523974 | — | 2 | 2 | no | — |
| 62 | C4⋊(C67⋊C8) | C23 | 1 | 2 | yes | — |
| 63 | #14523966 | — | 2 | 2 | no | — |
| 64 | #14523965 | — | 2 | 2 | no | — |
| 65 | #14523964 | — | 2 | 2 | no | — |
| 66 | #14523964 | D4 | 1 | 2 | yes | — |
| 67 | #14523963 | D4 | 1 | 2 | yes | — |
| 68 | C22⋊(C67⋊C8) | — | 2 | 2 | no | — |
| 69 | (C2×D67)⋊C8 | — | 2 | 2 | no | — |
| 70 | C4×C67⋊C8 | C23 | 1 | 2 | yes | — |
| 71 | C22×D4×C67 | — | 2 | 2 | no | — |
| 72 | C2×SD16×C67 | — | 4 | 1 | no | — |
| 73 | C4⋊Q8×C67 | C23 | 1 | 1 | yes | characteristic |
| 74 | #127×C67 | C23 | 1 | 1 | yes | characteristic |
| 75 | #121×C67 | — | 2 | 2 | no | — |
| 76 | #120×C67 | — | 4 | 1 | no | — |
| 77 | C4×D4×C67 | C23 | 1 | 2 | yes | — |
| 78 | #106×C67 | — | 2 | 2 | no | — |
| 79 | C4⋊C8×C67 | C23 | 1 | 2 | yes | — |
| 80 | #102×C67 | — | 2 | 2 | no | — |
| 81 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 82 | #11761628 | — | 4 | 4 | no | — |
| 83 | #11761628 | — | 8 | 2 | no | — |
| 84 | C2×Dic134 | — | 2 | 2 | no | — |
| 85 | C2×D268 | — | 4 | 1 | no | — |
| 86 | C2×D268 | C2×D4 | 1 | 2 | yes | — |
| 87 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 88 | C2×C4×D67 | — | 2 | 2 | no | — |
| 89 | C2×C4×D67 | — | 4 | 2 | no | — |
| 90 | #11761616 | — | 4 | 4 | no | — |
| 91 | #11761616 | — | 4 | 4 | no | — |
| 92 | #11761616 | — | 8 | 2 | no | — |
| 93 | #11761613 | — | 2 | 4 | no | — |
| 94 | #11761613 | — | 4 | 4 | no | — |
| 95 | #11761612 | — | 4 | 4 | no | — |
| 96 | #11761611 | — | 4 | 4 | no | — |
| 97 | C2×C67⋊C8 | — | 2 | 2 | no | — |
| 98 | C2×C67⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 99 | C2×C67⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 100 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 101 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 102 | C4⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 103 | Dic67⋊C4 | — | 4 | 2 | no | — |
| 104 | C22⋊Dic67 | — | 4 | 2 | no | — |
| 105 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 106 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 107 | C4×Dic67 | — | 4 | 1 | no | — |
| 108 | C24×C67 | — | 4 | 1 | no | — |
| 109 | C2×Q8×C67 | — | 2 | 1 | no | — |
| 110 | C2×D4×C67 | — | 2 | 2 | no | — |
| 111 | C2×D4×C67 | — | 2 | 1 | no | — |
| 112 | C2×D4×C67 | — | 4 | 2 | no | — |
| 113 | C2×D4×C67 | — | 4 | 4 | no | — |
| 114 | C2×D4×C67 | — | 8 | 2 | no | — |
| 115 | C2×D4×C67 | C2×D4 | 1 | 2 | yes | — |
| 116 | C22×C4×C67 | — | 2 | 2 | no | — |
| 117 | SD16×C67 | — | 8 | 2 | no | — |
| 118 | C2×C8×C67 | — | 2 | 1 | no | — |
| 119 | C2×C8×C67 | — | 2 | 2 | no | — |
| 120 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 121 | C4⋊C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 122 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 123 | C22⋊C4×C67 | — | 4 | 1 | no | — |
| 124 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 125 | C23×C67 | — | 2 | 2 | no | — |
| 126 | C23×C67 | — | 4 | 1 | no | — |
| 127 | C23×C67 | — | 8 | 4 | no | — |
| 128 | C23×C67 | — | 16 | 1 | no | — |
| 129 | C22×D67 | — | 2 | 2 | no | — |
| 130 | Q8×C67 | — | 8 | 1 | no | — |
| 131 | D4×C67 | — | 2 | 2 | no | — |
| 132 | D4×C67 | — | 2 | 2 | no | — |
| 133 | D4×C67 | — | 4 | 2 | no | — |
| 134 | D4×C67 | — | 4 | 2 | no | — |
| 135 | D4×C67 | — | 8 | 1 | no | — |
| 136 | D4×C67 | — | 8 | 4 | no | — |
| 137 | C2×C4×C67 | — | 2 | 2 | no | — |
| 138 | C2×C4×C67 | — | 4 | 2 | no | — |
| 139 | C2×C4×C67 | — | 4 | 2 | no | — |
| 140 | C2×C4×C67 | — | 4 | 1 | no | — |
| 141 | C2×C4×C67 | C22×D4 | 1 | 2 | yes | — |
| 142 | C2×C4×C67 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 143 | C22⋊D67 | — | 8 | 4 | no | — |
| 144 | C2×Dic67 | — | 2 | 2 | no | — |
| 145 | C2×Dic67 | — | 4 | 2 | no | — |
| 146 | D268 | — | 2 | 2 | no | — |
| 147 | D268 | — | 2 | 2 | no | — |
| 148 | D268 | — | 16 | 1 | no | — |
| 149 | C4×D67 | — | 4 | 2 | no | — |
| 150 | C4×D67 | — | 4 | 2 | no | — |
| 151 | C4×D67 | — | 8 | 4 | no | — |
| 152 | Dic134 | — | 4 | 2 | no | — |
| 153 | Dic134 | — | 4 | 2 | no | — |
| 154 | C8×C67 | — | 2 | 2 | no | — |
| 155 | C8×C67 | — | 4 | 2 | no | — |
| 156 | C67⋊C8 | — | 2 | 2 | no | — |
| 157 | C67⋊C8 | — | 4 | 2 | no | — |
| 158 | C67⋊C8 | AGL(1,ℤ/8) | 1 | 4 | yes | complemented |
| 159 | C22×C67 | — | 4 | 2 | no | — |
| 160 | C22×C67 | — | 4 | 2 | no | — |
| 161 | C22×C67 | — | 4 | 2 | no | — |
| 162 | C22×C67 | — | 8 | 2 | no | — |
| 163 | C22×C67 | — | 8 | 1 | no | — |
| 164 | C22×C67 | — | 16 | 4 | no | — |
| 165 | C22×C67 | D42 | 1 | 1 | yes | characteristic |
| 166 | C2×D67 | — | 4 | 2 | no | — |
| 167 | C2×D67 | — | 4 | 2 | no | — |
| 168 | C2×D67 | — | 4 | 2 | no | — |
| 169 | C4×C67 | — | 2 | 1 | no | — |
| 170 | C4×C67 | — | 4 | 2 | no | — |
| 171 | C4×C67 | — | 8 | 1 | no | — |
| 172 | C4×C67 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 173 | C4×C67 | #577 | 1 | 2 | yes | — |
| 174 | Dic67 | — | 4 | 2 | no | — |
| 175 | Dic67 | — | 8 | 2 | no | — |
| 176 | #20314 | — | 67 | 1 | no | maximal, Sylow |
| 177 | C2×C67 | — | 8 | 2 | no | — |
| 178 | C2×C67 | — | 16 | 1 | no | — |
| 179 | C2×C67 | #3272 | 1 | 2 | yes | — |
| 180 | C2×C67 | #3291 | 1 | 1 | yes | characteristic |
| 181 | D67 | — | 8 | 2 | no | — |
| 182 | #3354 | — | 67 | 2 | no | — |
| 183 | #3272 | — | 67 | 2 | no | — |
| 184 | #1705 | — | 67 | 1 | no | — |
| 185 | #1691 | — | 67 | 2 | no | — |
| 186 | #1685 | — | 67 | 2 | no | — |
| 187 | #1654 | — | 67 | 2 | no | — |
| 188 | #1629 | D67 | 1 | 1 | yes | characteristic, complemented |
| 189 | #1624 | — | 67 | 1 | no | — |
| 190 | #1589 | — | 67 | 2 | no | — |
| 191 | C67 | #20314 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 192 | C2×AGL(1,ℤ/8) | — | 134 | 2 | no | — |
| 193 | #555 | — | 67 | 1 | no | — |
| 194 | #547 | — | 67 | 2 | no | — |
| 195 | D42 | C2×D67 | 1 | 1 | yes | characteristic |
| 196 | #498 | — | 67 | 2 | no | — |
| 197 | #498 | — | 67 | 1 | no | — |
| 198 | #492 | — | 67 | 2 | no | — |
| 199 | #492 | C2×D67 | 1 | 1 | yes | characteristic |
| 200 | #482 | — | 134 | 2 | no | — |
| 201 | #481 | — | 134 | 2 | no | — |
| 202 | #476 | C2×D67 | 1 | 2 | yes | — |
| 203 | #474 | — | 67 | 2 | no | — |
| 204 | #469 | — | 134 | 2 | no | — |
| 205 | #468 | — | 134 | 2 | no | — |
| 206 | #461 | — | 67 | 2 | no | — |
| 207 | #459 | — | 67 | 2 | no | — |
| 208 | #450 | — | 134 | 2 | no | — |
| 209 | #449 | — | 134 | 2 | no | — |
| 210 | C4×D8 | — | 67 | 2 | no | — |
| 211 | #436 | — | 67 | 2 | no | — |
| 212 | #436 | — | 67 | 2 | no | — |
| 213 | #428 | — | 134 | 2 | no | — |
| 214 | #335 | — | 67 | 2 | no | — |
| 215 | #333 | — | 67 | 1 | no | — |
| 216 | #332 | — | 67 | 2 | no | — |
| 217 | #331 | C2×D67 | 1 | 1 | yes | characteristic |
| 218 | D4⋊C8 | — | 67 | 2 | no | — |
| 219 | D4⋊C8 | C2×D67 | 1 | 2 | yes | — |
| 220 | C82 | — | 67 | 1 | no | — |
| 221 | C2×#41 | — | 134 | 2 | no | — |
| 222 | C22×D4 | — | 2 | 2 | no | — |
| 223 | AGL(1,ℤ/8) | — | 268 | 8 | no | — |
| 224 | C2×SD16 | — | 4 | 1 | no | — |
| 225 | C2×SD16 | — | 134 | 2 | no | — |
| 226 | C2×SD16 | — | 134 | 2 | no | — |
| 227 | C2×SD16 | — | 134 | 2 | no | — |
| 228 | C2×D8 | — | 67 | 2 | no | — |
| 229 | C2×D8 | — | 134 | 2 | no | — |
| 230 | C2×M16 | — | 134 | 2 | no | — |
| 231 | C2×M16 | — | 134 | 2 | no | — |
| 232 | C4⋊Q8 | — | 67 | 2 | no | — |
| 233 | C4⋊Q8 | C22×D67 | 1 | 1 | yes | characteristic |
| 234 | #127 | C22×D67 | 1 | 1 | yes | characteristic |
| 235 | #124 | — | 268 | 1 | no | — |
| 236 | #123 | — | 268 | 2 | no | — |
| 237 | C22⋊Q8 | — | 134 | 2 | no | — |
| 238 | #121 | — | 2 | 2 | no | — |
| 239 | #121 | — | 134 | 2 | no | — |
| 240 | #121 | — | 134 | 2 | no | — |
| 241 | #120 | — | 4 | 1 | no | — |
| 242 | C4×D4 | — | 67 | 2 | no | — |
| 243 | C4×D4 | C22×D67 | 1 | 2 | yes | — |
| 244 | #117 | — | 134 | 2 | no | — |
| 245 | C2×C4⋊C4 | — | 134 | 2 | no | — |
| 246 | #107 | — | 67 | 2 | no | — |
| 247 | #107 | — | 134 | 2 | no | — |
| 248 | #106 | — | 2 | 2 | no | — |
| 249 | #106 | — | 268 | 1 | no | — |
| 250 | #106 | — | 134 | 2 | no | — |
| 251 | #106 | — | 134 | 2 | no | — |
| 252 | C4⋊C8 | — | 67 | 2 | no | — |
| 253 | C4⋊C8 | C22×D67 | 1 | 2 | yes | — |
| 254 | #103 | — | 134 | 2 | no | — |
| 255 | #102 | — | 2 | 2 | no | — |
| 256 | #102 | — | 67 | 2 | no | — |
| 257 | #102 | — | 67 | 2 | no | — |
| 258 | #102 | — | 134 | 2 | no | — |
| 259 | #102 | — | 134 | 2 | no | — |
| 260 | C22⋊C8 | — | 134 | 2 | no | — |
| 261 | C22⋊C8 | — | 134 | 2 | no | — |
| 262 | C4×C8 | — | 67 | 2 | no | — |
| 263 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 264 | C24 | — | 4 | 1 | no | — |
| 265 | #41 | — | 268 | 4 | no | — |
| 266 | #41 | — | 536 | 2 | no | — |
| 267 | C2×Q8 | — | 2 | 1 | no | — |
| 268 | C2×Q8 | — | 134 | 2 | no | — |
| 269 | C2×D4 | — | 2 | 2 | no | — |
| 270 | C2×D4 | — | 2 | 1 | no | — |
| 271 | C2×D4 | — | 4 | 2 | no | — |
| 272 | C2×D4 | — | 4 | 4 | no | — |
| 273 | C2×D4 | — | 8 | 2 | no | — |
| 274 | C2×D4 | — | 268 | 1 | no | — |
| 275 | C2×D4 | — | 268 | 2 | no | — |
| 276 | C2×D4 | — | 67 | 2 | no | — |
| 277 | C2×D4 | D4×D67 | 1 | 2 | yes | — |
| 278 | C22×C4 | — | 2 | 2 | no | — |
| 279 | C22×C4 | — | 268 | 2 | no | — |
| 280 | C22×C4 | — | 134 | 2 | no | — |
| 281 | SD16 | — | 8 | 2 | no | — |
| 282 | SD16 | — | 268 | 4 | no | — |
| 283 | SD16 | — | 268 | 4 | no | — |
| 284 | SD16 | — | 536 | 2 | no | — |
| 285 | D8 | — | 268 | 4 | no | — |
| 286 | D8 | — | 134 | 4 | no | — |
| 287 | M16 | — | 268 | 4 | no | — |
| 288 | M16 | — | 268 | 4 | no | — |
| 289 | C2×C8 | — | 2 | 1 | no | — |
| 290 | C2×C8 | — | 2 | 2 | no | — |
| 291 | C2×C8 | — | 67 | 2 | no | — |
| 292 | C2×C8 | — | 67 | 2 | no | — |
| 293 | C2×C8 | — | 134 | 2 | no | — |
| 294 | C4⋊C4 | — | 2 | 2 | no | — |
| 295 | C4⋊C4 | — | 268 | 2 | no | — |
| 296 | C4⋊C4 | — | 67 | 2 | no | — |
| 297 | C4⋊C4 | — | 134 | 2 | no | — |
| 298 | C4⋊C4 | — | 134 | 2 | no | — |
| 299 | C4⋊C4 | D4×D67 | 1 | 2 | yes | — |
| 300 | C22⋊C4 | — | 2 | 2 | no | — |
| 301 | C22⋊C4 | — | 4 | 1 | no | — |
| 302 | C22⋊C4 | — | 268 | 2 | no | — |
| 303 | C22⋊C4 | — | 268 | 2 | no | — |
| 304 | C22⋊C4 | — | 134 | 2 | no | — |
| 305 | C42 | — | 268 | 1 | no | — |
| 306 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 307 | C23 | — | 2 | 2 | no | — |
| 308 | C23 | — | 4 | 1 | no | — |
| 309 | C23 | — | 8 | 4 | no | — |
| 310 | C23 | — | 16 | 1 | no | — |
| 311 | C23 | — | 134 | 2 | no | — |
| 312 | Q8 | — | 8 | 1 | no | — |
| 313 | Q8 | — | 268 | 2 | no | — |
| 314 | Q8 | — | 268 | 2 | no | — |
| 315 | D4 | — | 2 | 2 | no | — |
| 316 | D4 | — | 2 | 2 | no | — |
| 317 | D4 | — | 4 | 2 | no | — |
| 318 | D4 | — | 4 | 2 | no | — |
| 319 | D4 | — | 8 | 1 | no | — |
| 320 | D4 | — | 8 | 4 | no | — |
| 321 | D4 | — | 536 | 4 | no | — |
| 322 | D4 | — | 1072 | 1 | no | — |
| 323 | D4 | — | 134 | 2 | no | — |
| 324 | D4 | — | 134 | 2 | no | — |
| 325 | C2×C4 | — | 2 | 2 | no | — |
| 326 | C2×C4 | — | 4 | 2 | no | — |
| 327 | C2×C4 | — | 4 | 2 | no | — |
| 328 | C2×C4 | — | 4 | 1 | no | — |
| 329 | C2×C4 | — | 268 | 2 | no | — |
| 330 | C2×C4 | — | 268 | 2 | no | — |
| 331 | C2×C4 | — | 268 | 2 | no | — |
| 332 | C2×C4 | — | 536 | 4 | no | — |
| 333 | C2×C4 | — | 134 | 2 | no | — |
| 334 | C2×C4 | C2×D4×D67 | 1 | 2 | yes | — |
| 335 | C2×C4 | #14524088 | 1 | 1 | yes | characteristic |
| 336 | C8 | — | 2 | 2 | no | — |
| 337 | C8 | — | 4 | 2 | no | — |
| 338 | C8 | — | 268 | 2 | no | — |
| 339 | C8 | — | 67 | 4 | no | — |
| 340 | C8 | — | 134 | 2 | no | — |
| 341 | C22 | — | 4 | 2 | no | — |
| 342 | C22 | — | 4 | 2 | no | — |
| 343 | C22 | — | 4 | 2 | no | — |
| 344 | C22 | — | 8 | 2 | no | — |
| 345 | C22 | — | 8 | 1 | no | — |
| 346 | C22 | — | 268 | 2 | no | — |
| 347 | C22 | — | 268 | 2 | no | — |
| 348 | C22 | — | 268 | 2 | no | — |
| 349 | C22 | — | 16 | 4 | no | — |
| 350 | C22 | #16864028 | 1 | 1 | yes | characteristic |
| 351 | C4 | — | 2 | 1 | no | — |
| 352 | C4 | — | 4 | 2 | no | — |
| 353 | C4 | — | 8 | 1 | no | — |
| 354 | C4 | — | 268 | 2 | no | — |
| 355 | C4 | — | 536 | 2 | no | — |
| 356 | C4 | AGL(1,ℤ/8)×D67 | 1 | 2 | yes | — |
| 357 | C4 | #16864202 | 1 | 2 | yes | — |
| 358 | C2 | — | 8 | 2 | no | — |
| 359 | C2 | — | 16 | 1 | no | — |
| 360 | C2 | — | 536 | 2 | no | — |
| 361 | C2 | #22571807 | 1 | 2 | yes | — |
| 362 | C2 | #22572004 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22572801 | C2 | semidirect |
| 2. #22571805 | C2 | semidirect |
| 3. #22559795 | C2 | semidirect |
| 4. #22559710 | C2 | semidirect |
| 5. #22559673 | C2 | semidirect |
| 6. #22559495 | C2 | semidirect |
| 7. #22559290 | C2 | semidirect |
| 8. #22559091 | C2 | semidirect |
| 9. C67×#1629 | C2 | semidirect |
| 11. #16864112 | C22 | semidirect |
| 13. #16863794 | C22 | semidirect |
| 14. #16863792 | C22 | semidirect |
| 18. #16863677 | C22 | semidirect |
| 27. #16863473 | C22 | semidirect |
| 29. #16863148 | C22 | semidirect |
| 30. #16863145 | C22 | semidirect |
| 31. #16863143 | C22 | semidirect |
| 32. #16863125 | C22 | semidirect |
| 33. C8×C67⋊C8 | C22 | semidirect |
| 158. C67⋊C8 | AGL(1,ℤ/8) | semidirect |
| 188. #1629 | D67 | semidirect |
| 191. C67 | #20314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22572801 | 2 |
| #22571805 | 2 |
| #22559795 | 2 |
| #22559710 | 2 |
| #22559673 | 2 |
| #22559495 | 2 |
| #22559290 | 2 |
| #22559091 | 2 |
| C67×#1629 | 2 |
| #20314 | 67 |