Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
754 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 754 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 | #22573255 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22571825 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22559823 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22559692 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22559686 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22559277 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22559266 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22559102 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C67×#1619 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#14524069 | — | 2 | 2 | no | — |
| 11 | #16864132 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #16864067 | C22 | 1 | 2 | yes | — |
| 13 | #16863784 | — | 2 | 2 | no | — |
| 14 | #16863773 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #16863772 | C22 | 1 | 2 | yes | — |
| 16 | #16863772 | C22 | 1 | 2 | yes | complemented |
| 17 | #16863647 | — | 2 | 2 | no | — |
| 18 | #16863610 | — | 2 | 2 | no | — |
| 19 | #16863597 | C22 | 1 | 2 | yes | complemented |
| 20 | #16863593 | C22 | 1 | 2 | yes | — |
| 21 | #16863591 | C22 | 1 | 2 | yes | — |
| 22 | #16863589 | — | 2 | 2 | no | — |
| 23 | #16863539 | — | 2 | 2 | no | — |
| 24 | #16863530 | — | 2 | 2 | no | — |
| 25 | #16863523 | C22 | 1 | 2 | yes | complemented |
| 26 | #16863505 | — | 2 | 2 | no | — |
| 27 | C4×#11761616 | C22 | 1 | 2 | yes | — |
| 28 | #16863474 | C22 | 1 | 2 | yes | — |
| 29 | #16863146 | C22 | 1 | 2 | yes | complemented |
| 30 | #16863140 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #16863139 | C22 | 1 | 2 | yes | complemented |
| 32 | #16863128 | C22 | 1 | 2 | yes | complemented |
| 33 | C8×C67⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | D42×C67 | C22 | 1 | 1 | yes | characteristic |
| 35 | #493×C67 | C22 | 1 | 1 | yes | characteristic |
| 36 | #459×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×#11761617 | — | 2 | 2 | no | — |
| 42 | C2×#11761616 | — | 2 | 2 | no | — |
| 43 | C2×#11761616 | D4 | 1 | 2 | yes | — |
| 44 | C2×D536 | — | 4 | 1 | no | — |
| 45 | C2×#11761613 | — | 2 | 2 | no | — |
| 46 | C2×#11761613 | — | 2 | 2 | no | — |
| 47 | C2×#11761613 | — | 2 | 2 | no | — |
| 48 | C2×#11761613 | — | 2 | 2 | no | — |
| 49 | C2×#11761613 | — | 2 | 2 | no | — |
| 50 | C2×#11761612 | — | 2 | 2 | no | — |
| 51 | #14524040 | C23 | 1 | 2 | yes | — |
| 52 | #14524039 | — | 2 | 2 | no | — |
| 53 | #14524030 | — | 2 | 2 | no | — |
| 54 | #14524024 | — | 4 | 1 | no | — |
| 55 | #14524017 | — | 2 | 2 | no | — |
| 56 | #14524016 | — | 4 | 2 | no | — |
| 57 | C4×Dic134 | C23 | 1 | 2 | yes | — |
| 58 | D4×Dic67 | — | 2 | 2 | no | — |
| 59 | #14524005 | — | 2 | 2 | no | — |
| 60 | #14523974 | D4 | 1 | 2 | yes | — |
| 61 | C4⋊(C67⋊C8) | C23 | 1 | 2 | yes | — |
| 62 | Dic67⋊C8 | — | 2 | 2 | no | — |
| 63 | #14523966 | D4 | 1 | 2 | yes | — |
| 64 | #14523965 | — | 2 | 2 | no | — |
| 65 | #14523964 | — | 2 | 2 | no | — |
| 66 | #14523964 | D4 | 1 | 2 | yes | — |
| 67 | #14523963 | — | 2 | 2 | no | — |
| 68 | C22⋊(C67⋊C8) | — | 2 | 2 | no | — |
| 69 | #14523953 | — | 2 | 2 | no | — |
| 70 | C4×C67⋊C8 | C23 | 1 | 2 | yes | — |
| 71 | C22×D4×C67 | — | 2 | 2 | no | — |
| 72 | C2×D8×C67 | — | 2 | 2 | no | — |
| 73 | C2×D8×C67 | — | 4 | 1 | no | — |
| 74 | #127×C67 | C23 | 1 | 1 | yes | characteristic |
| 75 | #127×C67 | C23 | 1 | 1 | yes | characteristic |
| 76 | #121×C67 | — | 2 | 2 | no | — |
| 77 | #120×C67 | — | 4 | 1 | no | — |
| 78 | C4×D4×C67 | C23 | 1 | 2 | yes | — |
| 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 | C2×D4 | 1 | 2 | yes | — |
| 85 | C2×D268 | — | 2 | 2 | no | — |
| 86 | C2×D268 | — | 2 | 2 | no | — |
| 87 | C2×D268 | — | 2 | 2 | no | — |
| 88 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 89 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 90 | C22×Dic67 | — | 4 | 1 | no | — |
| 91 | C2×C4×D67 | — | 4 | 2 | no | — |
| 92 | #11761617 | — | 8 | 2 | no | — |
| 93 | #11761616 | — | 2 | 4 | no | — |
| 94 | #11761616 | — | 4 | 4 | no | — |
| 95 | D536 | — | 8 | 2 | no | — |
| 96 | #11761613 | — | 4 | 4 | no | — |
| 97 | #11761613 | — | 4 | 4 | no | — |
| 98 | #11761613 | — | 4 | 4 | no | — |
| 99 | #11761613 | — | 8 | 2 | no | — |
| 100 | #11761613 | — | 8 | 2 | no | — |
| 101 | #11761612 | — | 4 | 4 | no | — |
| 102 | C2×C67⋊C8 | — | 2 | 2 | no | — |
| 103 | C2×C67⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 104 | C2×C67⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 105 | C4⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 106 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 107 | C22⋊Dic67 | — | 4 | 2 | no | — |
| 108 | C22⋊Dic67 | — | 4 | 1 | no | — |
| 109 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 110 | C4×Dic67 | — | 2 | 2 | no | — |
| 111 | C24×C67 | — | 4 | 1 | no | — |
| 112 | C2×D4×C67 | — | 2 | 2 | no | — |
| 113 | C2×D4×C67 | — | 2 | 2 | no | — |
| 114 | C2×D4×C67 | — | 2 | 1 | no | — |
| 115 | C2×D4×C67 | — | 2 | 1 | no | — |
| 116 | C2×D4×C67 | — | 4 | 2 | no | — |
| 117 | C2×D4×C67 | — | 4 | 4 | no | — |
| 118 | C2×D4×C67 | — | 8 | 2 | no | — |
| 119 | C2×D4×C67 | C2×D4 | 1 | 2 | yes | — |
| 120 | C22×C4×C67 | — | 2 | 2 | no | — |
| 121 | D8×C67 | — | 8 | 2 | no | — |
| 122 | D8×C67 | — | 8 | 2 | no | — |
| 123 | C2×C8×C67 | — | 2 | 1 | no | — |
| 124 | C2×C8×C67 | — | 2 | 2 | no | — |
| 125 | C4⋊C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 126 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 127 | C22⋊C4×C67 | — | 4 | 1 | no | — |
| 128 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 129 | C23×C67 | — | 2 | 2 | no | — |
| 130 | C23×C67 | — | 4 | 1 | no | — |
| 131 | C23×C67 | — | 4 | 1 | no | — |
| 132 | C23×C67 | — | 8 | 4 | no | — |
| 133 | C23×C67 | — | 16 | 1 | no | — |
| 134 | C22×D67 | — | 4 | 2 | no | — |
| 135 | D4×C67 | — | 2 | 2 | no | — |
| 136 | D4×C67 | — | 2 | 2 | no | — |
| 137 | D4×C67 | — | 4 | 2 | no | — |
| 138 | D4×C67 | — | 4 | 2 | no | — |
| 139 | D4×C67 | — | 4 | 2 | no | — |
| 140 | D4×C67 | — | 4 | 2 | no | — |
| 141 | D4×C67 | — | 8 | 1 | no | — |
| 142 | D4×C67 | — | 8 | 1 | no | — |
| 143 | D4×C67 | — | 8 | 4 | no | — |
| 144 | C2×C4×C67 | — | 2 | 2 | no | — |
| 145 | C2×C4×C67 | — | 4 | 2 | no | — |
| 146 | C2×C4×C67 | — | 4 | 2 | no | — |
| 147 | C2×C4×C67 | C22×D4 | 1 | 2 | yes | — |
| 148 | C2×C4×C67 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 149 | C22⋊D67 | — | 8 | 4 | no | — |
| 150 | C22⋊D67 | — | 16 | 2 | no | — |
| 151 | C2×Dic67 | — | 2 | 2 | no | — |
| 152 | C2×Dic67 | — | 2 | 2 | no | — |
| 153 | C2×Dic67 | — | 16 | 1 | no | — |
| 154 | D268 | — | 4 | 2 | no | — |
| 155 | D268 | — | 4 | 2 | no | — |
| 156 | D268 | — | 4 | 2 | no | — |
| 157 | D268 | — | 4 | 2 | no | — |
| 158 | D268 | — | 8 | 2 | no | — |
| 159 | C4×D67 | — | 8 | 4 | no | — |
| 160 | Dic134 | — | 2 | 2 | no | — |
| 161 | Dic134 | — | 2 | 2 | no | — |
| 162 | C8×C67 | — | 2 | 2 | no | — |
| 163 | C8×C67 | — | 4 | 2 | no | — |
| 164 | C67⋊C8 | — | 2 | 2 | no | — |
| 165 | C67⋊C8 | — | 4 | 2 | no | — |
| 166 | C67⋊C8 | AGL(1,ℤ/8) | 1 | 4 | yes | complemented |
| 167 | C22×C67 | — | 4 | 2 | no | — |
| 168 | C22×C67 | — | 4 | 2 | no | — |
| 169 | C22×C67 | — | 4 | 2 | no | — |
| 170 | C22×C67 | — | 8 | 2 | no | — |
| 171 | C22×C67 | — | 8 | 2 | no | — |
| 172 | C22×C67 | — | 8 | 1 | no | — |
| 173 | C22×C67 | — | 8 | 1 | no | — |
| 174 | C22×C67 | — | 16 | 4 | no | — |
| 175 | C22×C67 | D42 | 1 | 1 | yes | characteristic |
| 176 | C2×D67 | — | 8 | 2 | no | — |
| 177 | C2×D67 | — | 8 | 2 | no | — |
| 178 | C2×D67 | — | 8 | 2 | no | — |
| 179 | C4×C67 | — | 2 | 1 | no | — |
| 180 | C4×C67 | — | 4 | 2 | no | — |
| 181 | C4×C67 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 182 | C4×C67 | #576 | 1 | 2 | yes | — |
| 183 | Dic67 | — | 4 | 2 | no | — |
| 184 | Dic67 | — | 4 | 2 | no | — |
| 185 | #20310 | — | 67 | 1 | no | maximal, Sylow |
| 186 | C2×C67 | — | 8 | 2 | no | — |
| 187 | C2×C67 | — | 16 | 1 | no | — |
| 188 | C2×C67 | — | 16 | 1 | no | — |
| 189 | C2×C67 | #3274 | 1 | 2 | yes | — |
| 190 | C2×C67 | #3292 | 1 | 1 | yes | characteristic |
| 191 | D67 | — | 16 | 2 | no | — |
| 192 | #3399 | — | 67 | 2 | no | — |
| 193 | #3274 | — | 67 | 2 | no | — |
| 194 | #1712 | — | 67 | 1 | no | — |
| 195 | #1688 | — | 67 | 2 | no | — |
| 196 | #1687 | — | 67 | 2 | no | — |
| 197 | #1621 | — | 67 | 2 | no | — |
| 198 | #1620 | — | 67 | 1 | no | — |
| 199 | #1619 | D67 | 1 | 1 | yes | characteristic, complemented |
| 200 | #1590 | — | 67 | 2 | no | — |
| 201 | C67 | #20310 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 202 | C2×AGL(1,ℤ/8) | — | 134 | 2 | no | — |
| 203 | #559 | — | 67 | 1 | no | — |
| 204 | #550 | — | 67 | 2 | no | — |
| 205 | D42 | C2×D67 | 1 | 1 | yes | characteristic |
| 206 | #496 | — | 134 | 2 | no | — |
| 207 | #493 | — | 67 | 2 | no | — |
| 208 | #493 | — | 67 | 2 | no | — |
| 209 | #493 | — | 67 | 1 | no | — |
| 210 | #493 | C2×D67 | 1 | 1 | yes | characteristic |
| 211 | #469 | — | 134 | 2 | no | — |
| 212 | #463 | — | 134 | 2 | no | — |
| 213 | #460 | — | 67 | 2 | no | — |
| 214 | #460 | — | 67 | 2 | no | — |
| 215 | #459 | — | 67 | 2 | no | — |
| 216 | #459 | — | 134 | 2 | no | — |
| 217 | #459 | C2×D67 | 1 | 2 | yes | — |
| 218 | #449 | — | 134 | 2 | no | — |
| 219 | #447 | — | 134 | 2 | no | — |
| 220 | #446 | — | 67 | 2 | no | — |
| 221 | #442 | — | 134 | 2 | no | — |
| 222 | C4×SD16 | — | 67 | 2 | no | — |
| 223 | #436 | — | 67 | 2 | no | — |
| 224 | #334 | — | 67 | 2 | no | — |
| 225 | #331 | — | 67 | 1 | no | — |
| 226 | #331 | — | 67 | 2 | no | — |
| 227 | #331 | C2×D67 | 1 | 1 | yes | characteristic |
| 228 | Q8⋊C8 | — | 67 | 2 | no | — |
| 229 | D4⋊C8 | C2×D67 | 1 | 2 | yes | — |
| 230 | C82 | — | 67 | 1 | no | — |
| 231 | C2×#41 | — | 134 | 2 | no | — |
| 232 | C22×D4 | — | 2 | 2 | no | — |
| 233 | AGL(1,ℤ/8) | — | 268 | 8 | no | — |
| 234 | C2×SD16 | — | 67 | 2 | no | — |
| 235 | C2×SD16 | — | 134 | 2 | no | — |
| 236 | C2×SD16 | — | 134 | 2 | no | — |
| 237 | C2×D8 | — | 2 | 2 | no | — |
| 238 | C2×D8 | — | 4 | 1 | no | — |
| 239 | C2×D8 | — | 268 | 1 | no | — |
| 240 | C2×D8 | — | 134 | 2 | no | — |
| 241 | C2×D8 | — | 134 | 2 | no | — |
| 242 | C2×D8 | — | 134 | 2 | no | — |
| 243 | C2×D8 | — | 134 | 2 | no | — |
| 244 | C2×D8 | — | 134 | 2 | no | — |
| 245 | C2×M16 | — | 134 | 2 | no | — |
| 246 | #127 | — | 67 | 2 | no | — |
| 247 | #127 | — | 134 | 2 | no | — |
| 248 | #127 | C22×D67 | 1 | 1 | yes | characteristic |
| 249 | #127 | C22×D67 | 1 | 1 | yes | characteristic |
| 250 | #124 | — | 134 | 2 | no | — |
| 251 | #123 | — | 268 | 1 | no | — |
| 252 | #121 | — | 2 | 2 | no | — |
| 253 | #121 | — | 268 | 2 | no | — |
| 254 | #121 | — | 134 | 2 | no | — |
| 255 | #120 | — | 4 | 1 | no | — |
| 256 | C4×Q8 | — | 67 | 2 | no | — |
| 257 | C4×D4 | — | 134 | 2 | no | — |
| 258 | C4×D4 | — | 134 | 2 | no | — |
| 259 | C4×D4 | C22×D67 | 1 | 2 | yes | — |
| 260 | #106 | — | 67 | 2 | no | — |
| 261 | C4⋊C8 | — | 67 | 2 | no | — |
| 262 | C4⋊C8 | — | 134 | 2 | no | — |
| 263 | C4⋊C8 | C22×D67 | 1 | 2 | yes | — |
| 264 | #103 | — | 67 | 2 | no | — |
| 265 | #102 | — | 2 | 2 | no | — |
| 266 | #102 | — | 67 | 2 | no | — |
| 267 | #102 | — | 134 | 2 | no | — |
| 268 | #102 | — | 134 | 2 | no | — |
| 269 | #102 | — | 134 | 2 | no | — |
| 270 | C22⋊C8 | — | 134 | 2 | no | — |
| 271 | #97 | — | 134 | 2 | no | — |
| 272 | C4×C8 | — | 67 | 2 | no | — |
| 273 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 274 | C24 | — | 4 | 1 | no | — |
| 275 | #41 | — | 268 | 4 | no | — |
| 276 | #41 | — | 536 | 2 | no | — |
| 277 | C2×Q8 | — | 67 | 2 | no | — |
| 278 | C2×D4 | — | 2 | 2 | no | — |
| 279 | C2×D4 | — | 2 | 2 | no | — |
| 280 | C2×D4 | — | 2 | 1 | no | — |
| 281 | C2×D4 | — | 2 | 1 | no | — |
| 282 | C2×D4 | — | 4 | 2 | no | — |
| 283 | C2×D4 | — | 4 | 4 | no | — |
| 284 | C2×D4 | — | 8 | 2 | no | — |
| 285 | C2×D4 | — | 268 | 2 | no | — |
| 286 | C2×D4 | — | 268 | 2 | no | — |
| 287 | C2×D4 | — | 134 | 2 | no | — |
| 288 | C2×D4 | — | 134 | 2 | no | — |
| 289 | C2×D4 | — | 134 | 2 | no | — |
| 290 | C2×D4 | D4×D67 | 1 | 2 | yes | — |
| 291 | C22×C4 | — | 2 | 2 | no | — |
| 292 | C22×C4 | — | 268 | 2 | no | — |
| 293 | C22×C4 | — | 268 | 1 | no | — |
| 294 | SD16 | — | 268 | 4 | no | — |
| 295 | SD16 | — | 536 | 2 | no | — |
| 296 | SD16 | — | 134 | 4 | no | — |
| 297 | D8 | — | 8 | 2 | no | — |
| 298 | D8 | — | 8 | 2 | no | — |
| 299 | D8 | — | 268 | 4 | no | — |
| 300 | D8 | — | 268 | 4 | no | — |
| 301 | D8 | — | 268 | 4 | no | — |
| 302 | D8 | — | 536 | 2 | no | — |
| 303 | D8 | — | 536 | 2 | no | — |
| 304 | D8 | — | 536 | 2 | no | — |
| 305 | M16 | — | 268 | 4 | no | — |
| 306 | C2×C8 | — | 2 | 1 | no | — |
| 307 | C2×C8 | — | 2 | 2 | no | — |
| 308 | C2×C8 | — | 67 | 2 | no | — |
| 309 | C2×C8 | — | 67 | 2 | no | — |
| 310 | C2×C8 | — | 134 | 2 | no | — |
| 311 | C4⋊C4 | — | 67 | 2 | no | — |
| 312 | C4⋊C4 | — | 134 | 2 | no | — |
| 313 | C4⋊C4 | D4×D67 | 1 | 2 | yes | — |
| 314 | C22⋊C4 | — | 2 | 2 | no | — |
| 315 | C22⋊C4 | — | 4 | 1 | no | — |
| 316 | C22⋊C4 | — | 268 | 2 | no | — |
| 317 | C22⋊C4 | — | 268 | 2 | no | — |
| 318 | C22⋊C4 | — | 268 | 1 | no | — |
| 319 | C42 | — | 134 | 2 | no | — |
| 320 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 321 | C23 | — | 2 | 2 | no | — |
| 322 | C23 | — | 4 | 1 | no | — |
| 323 | C23 | — | 4 | 1 | no | — |
| 324 | C23 | — | 8 | 4 | no | — |
| 325 | C23 | — | 268 | 2 | no | — |
| 326 | C23 | — | 16 | 1 | no | — |
| 327 | Q8 | — | 134 | 2 | no | — |
| 328 | Q8 | — | 134 | 2 | no | — |
| 329 | D4 | — | 2 | 2 | no | — |
| 330 | D4 | — | 2 | 2 | no | — |
| 331 | D4 | — | 4 | 2 | no | — |
| 332 | D4 | — | 4 | 2 | no | — |
| 333 | D4 | — | 4 | 2 | no | — |
| 334 | D4 | — | 4 | 2 | no | — |
| 335 | D4 | — | 8 | 1 | no | — |
| 336 | D4 | — | 8 | 1 | no | — |
| 337 | D4 | — | 8 | 4 | no | — |
| 338 | D4 | — | 268 | 2 | no | — |
| 339 | D4 | — | 268 | 2 | no | — |
| 340 | D4 | — | 268 | 2 | no | — |
| 341 | D4 | — | 268 | 2 | no | — |
| 342 | D4 | — | 536 | 2 | no | — |
| 343 | D4 | — | 536 | 4 | no | — |
| 344 | D4 | — | 1072 | 2 | no | — |
| 345 | C2×C4 | — | 2 | 2 | no | — |
| 346 | C2×C4 | — | 4 | 2 | no | — |
| 347 | C2×C4 | — | 4 | 2 | no | — |
| 348 | C2×C4 | — | 536 | 4 | no | — |
| 349 | C2×C4 | — | 1072 | 1 | no | — |
| 350 | C2×C4 | — | 134 | 2 | no | — |
| 351 | C2×C4 | — | 134 | 2 | no | — |
| 352 | C2×C4 | C2×D4×D67 | 1 | 2 | yes | — |
| 353 | C2×C4 | #14524088 | 1 | 1 | yes | characteristic |
| 354 | C8 | — | 2 | 2 | no | — |
| 355 | C8 | — | 4 | 2 | no | — |
| 356 | C8 | — | 268 | 2 | no | — |
| 357 | C8 | — | 67 | 4 | no | — |
| 358 | C8 | — | 134 | 2 | no | — |
| 359 | C22 | — | 4 | 2 | no | — |
| 360 | C22 | — | 4 | 2 | no | — |
| 361 | C22 | — | 4 | 2 | no | — |
| 362 | C22 | — | 8 | 2 | no | — |
| 363 | C22 | — | 8 | 2 | no | — |
| 364 | C22 | — | 8 | 1 | no | — |
| 365 | C22 | — | 8 | 1 | no | — |
| 366 | C22 | — | 16 | 4 | no | — |
| 367 | C22 | — | 536 | 2 | no | — |
| 368 | C22 | — | 536 | 2 | no | — |
| 369 | C22 | — | 536 | 2 | no | — |
| 370 | C22 | #16864028 | 1 | 1 | yes | characteristic |
| 371 | C4 | — | 2 | 1 | no | — |
| 372 | C4 | — | 4 | 2 | no | — |
| 373 | C4 | — | 268 | 2 | no | — |
| 374 | C4 | — | 268 | 2 | no | — |
| 375 | C4 | AGL(1,ℤ/8)×D67 | 1 | 2 | yes | — |
| 376 | C4 | #16864197 | 1 | 2 | yes | — |
| 377 | C2 | — | 8 | 2 | no | — |
| 378 | C2 | — | 16 | 1 | no | — |
| 379 | C2 | — | 16 | 1 | no | — |
| 380 | C2 | — | 1072 | 2 | no | — |
| 381 | C2 | #22571827 | 1 | 2 | yes | — |
| 382 | C2 | #22572005 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22573255 | C2 | semidirect |
| 2. #22571825 | C2 | semidirect |
| 3. #22559823 | C2 | semidirect |
| 4. #22559692 | C2 | semidirect |
| 5. #22559686 | C2 | semidirect |
| 6. #22559277 | C2 | semidirect |
| 7. #22559266 | C2 | semidirect |
| 8. #22559102 | C2 | semidirect |
| 9. C67×#1619 | C2 | semidirect |
| 11. #16864132 | C22 | semidirect |
| 14. #16863773 | C22 | semidirect |
| 16. #16863772 | C22 | semidirect |
| 19. #16863597 | C22 | semidirect |
| 25. #16863523 | C22 | semidirect |
| 29. #16863146 | C22 | semidirect |
| 30. #16863140 | C22 | semidirect |
| 31. #16863139 | C22 | semidirect |
| 32. #16863128 | C22 | semidirect |
| 33. C8×C67⋊C8 | C22 | semidirect |
| 166. C67⋊C8 | AGL(1,ℤ/8) | semidirect |
| 199. #1619 | D67 | semidirect |
| 201. C67 | #20310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573255 | 2 |
| #22571825 | 2 |
| #22559823 | 2 |
| #22559692 | 2 |
| #22559686 | 2 |
| #22559277 | 2 |
| #22559266 | 2 |
| #22559102 | 2 |
| C67×#1619 | 2 |
| #20310 | 67 |