Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
426 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 53 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 | #22571052 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22562159 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22562157 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22561277 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22558193 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22558144 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C67×#1340 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16864196 | C22 | 1 | 1 | yes | characteristic |
| 9 | #16863909 | — | 2 | 1 | no | — |
| 10 | #16863908 | — | 2 | 1 | no | — |
| 11 | #16863837 | — | 2 | 1 | no | — |
| 12 | #16863834 | — | 2 | 1 | no | — |
| 13 | #16863735 | — | 2 | 1 | no | — |
| 14 | #16863722 | — | 2 | 1 | no | — |
| 15 | #16863649 | C22 | 1 | 1 | yes | characteristic |
| 16 | #16863644 | — | 2 | 1 | no | — |
| 17 | #16863557 | — | 2 | 1 | no | — |
| 18 | #16863544 | — | 2 | 1 | no | — |
| 19 | #16863414 | — | 2 | 1 | no | — |
| 20 | #16863359 | C22 | 1 | 1 | yes | characteristic |
| 21 | #16863207 | — | 2 | 1 | no | — |
| 22 | #16863205 | — | 2 | 1 | no | — |
| 23 | #16863178 | C22 | 1 | 1 | yes | characteristic |
| 24 | #470×C67 | C22 | 1 | 1 | yes | characteristic |
| 25 | #349×C67 | C22 | 1 | 1 | yes | characteristic |
| 26 | H(3,ℤ/4)×C67 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#11761629 | — | 2 | 1 | no | — |
| 28 | C2×#11761628 | — | 2 | 1 | no | — |
| 29 | C22×C4×D67 | D4 | 1 | 1 | yes | characteristic |
| 30 | #14524076 | — | 4 | 1 | no | — |
| 31 | #14524071 | — | 4 | 1 | no | — |
| 32 | #14524065 | — | 2 | 1 | no | — |
| 33 | #14524065 | — | 2 | 1 | no | — |
| 34 | C2×#11761615 | — | 2 | 1 | no | — |
| 35 | C2×D536 | D4 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×#11761612 | D4 | 1 | 1 | yes | characteristic |
| 37 | #14524028 | — | 4 | 1 | no | — |
| 38 | #14524027 | — | 4 | 1 | no | — |
| 39 | #14524023 | — | 4 | 1 | no | — |
| 40 | #14524019 | — | 2 | 1 | no | — |
| 41 | #14524018 | — | 2 | 1 | no | — |
| 42 | #14524018 | — | 4 | 1 | no | — |
| 43 | #14524017 | — | 2 | 1 | no | — |
| 44 | #14524013 | — | 4 | 1 | no | — |
| 45 | #14524013 | — | 4 | 1 | no | — |
| 46 | C4×D268 | — | 4 | 2 | no | — |
| 47 | #14524005 | — | 4 | 1 | no | — |
| 48 | (C22⋊D67)⋊C4 | — | 4 | 1 | no | — |
| 49 | #14524001 | — | 2 | 1 | no | — |
| 50 | #14523989 | — | 4 | 1 | no | — |
| 51 | #14523988 | — | 4 | 1 | no | — |
| 52 | #14523986 | — | 4 | 1 | no | — |
| 53 | D1072 | — | 4 | 1 | no | — |
| 54 | #14523983 | — | 2 | 1 | no | — |
| 55 | #14523976 | — | 2 | 1 | no | — |
| 56 | #14523975 | D4 | 1 | 1 | yes | characteristic, complemented |
| 57 | #14523971 | — | 4 | 2 | no | — |
| 58 | #14523967 | — | 2 | 1 | no | — |
| 59 | #14523965 | — | 2 | 1 | no | — |
| 60 | #14523963 | — | 2 | 1 | no | — |
| 61 | (C2×D67)⋊C8 | — | 2 | 1 | no | — |
| 62 | (C2×D67)⋊C8 | — | 2 | 1 | no | — |
| 63 | C2×Q16×C67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 64 | C2×M16×C67 | C23 | 1 | 1 | yes | characteristic |
| 65 | C22⋊Q8×C67 | — | 2 | 1 | no | — |
| 66 | #117×C67 | — | 2 | 1 | no | — |
| 67 | M32×C67 | — | 2 | 1 | no | — |
| 68 | #106×C67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 69 | #103×C67 | — | 2 | 1 | no | — |
| 70 | C23×D67 | D8 | 1 | 1 | yes | characteristic |
| 71 | #11761629 | — | 8 | 1 | no | — |
| 72 | #11761629 | — | 8 | 1 | no | — |
| 73 | #11761628 | — | 4 | 1 | no | — |
| 74 | #11761628 | — | 4 | 1 | no | — |
| 75 | #11761628 | — | 4 | 1 | no | — |
| 76 | #11761628 | — | 4 | 1 | no | — |
| 77 | C2×Dic134 | — | 2 | 1 | no | — |
| 78 | C2×D268 | — | 2 | 1 | no | — |
| 79 | C2×D268 | — | 2 | 1 | no | — |
| 80 | C2×D268 | — | 4 | 1 | no | — |
| 81 | C2×D268 | — | 4 | 1 | no | — |
| 82 | C2×D268 | — | 4 | 2 | no | — |
| 83 | C2×C22⋊D67 | — | 4 | 1 | no | — |
| 84 | C2×C22⋊D67 | — | 4 | 1 | no | — |
| 85 | C22×Dic67 | D8 | 1 | 1 | yes | characteristic |
| 86 | C2×C4×D67 | — | 2 | 1 | no | — |
| 87 | C2×C4×D67 | — | 2 | 1 | no | — |
| 88 | C2×C4×D67 | — | 4 | 1 | no | — |
| 89 | C2×C4×D67 | — | 4 | 1 | no | — |
| 90 | C2×C4×D67 | — | 4 | 1 | no | — |
| 91 | C2×C4×D67 | — | 4 | 1 | no | — |
| 92 | Dic268 | — | 2 | 1 | no | — |
| 93 | Dic268 | — | 2 | 1 | no | — |
| 94 | #11761617 | — | 4 | 1 | no | — |
| 95 | #11761617 | — | 4 | 1 | no | — |
| 96 | #11761615 | — | 8 | 1 | no | — |
| 97 | D536 | — | 2 | 1 | no | — |
| 98 | D536 | — | 2 | 1 | no | — |
| 99 | D536 | — | 4 | 1 | no | — |
| 100 | #11761612 | — | 4 | 1 | no | — |
| 101 | C2×C67⋊C8 | — | 2 | 1 | no | — |
| 102 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 103 | C4⋊Dic67 | — | 4 | 2 | no | — |
| 104 | Dic67⋊C4 | — | 4 | 1 | no | — |
| 105 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 106 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 107 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 108 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 109 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 110 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 111 | C4×Dic67 | — | 4 | 1 | no | — |
| 112 | C67⋊C16 | — | 4 | 1 | no | — |
| 113 | C2×Q8×C67 | — | 2 | 1 | no | — |
| 114 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | Q16×C67 | — | 4 | 1 | no | — |
| 116 | M16×C67 | — | 4 | 1 | no | — |
| 117 | C2×C8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C2×C8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 120 | C4⋊C4×C67 | — | 4 | 1 | no | — |
| 121 | C4⋊C4×C67 | — | 4 | 1 | no | — |
| 122 | C22⋊C4×C67 | — | 4 | 1 | no | — |
| 123 | C22⋊C4×C67 | — | 4 | 1 | no | — |
| 124 | C42×C67 | — | 2 | 2 | no | — |
| 125 | C16×C67 | — | 4 | 1 | no | — |
| 126 | C23×C67 | C2×D8 | 1 | 1 | yes | characteristic |
| 127 | C22×D67 | — | 2 | 1 | no | — |
| 128 | C22×D67 | — | 4 | 1 | no | — |
| 129 | C22×D67 | — | 4 | 1 | no | — |
| 130 | C22×D67 | — | 4 | 1 | no | — |
| 131 | C22×D67 | — | 8 | 1 | no | — |
| 132 | Q8×C67 | — | 4 | 1 | no | — |
| 133 | Q8×C67 | — | 4 | 1 | no | — |
| 134 | C2×C4×C67 | — | 2 | 1 | no | — |
| 135 | C2×C4×C67 | — | 2 | 1 | no | — |
| 136 | C2×C4×C67 | — | 4 | 2 | no | — |
| 137 | C2×C4×C67 | — | 4 | 1 | no | — |
| 138 | C2×C4×C67 | — | 4 | 1 | no | — |
| 139 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 140 | C2×C4×C67 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 141 | C22⋊D67 | — | 8 | 1 | no | — |
| 142 | C22⋊D67 | — | 8 | 2 | no | — |
| 143 | C22⋊D67 | — | 8 | 1 | no | — |
| 144 | C2×Dic67 | — | 2 | 1 | no | — |
| 145 | C2×Dic67 | — | 4 | 1 | no | — |
| 146 | C2×Dic67 | — | 4 | 1 | no | — |
| 147 | C2×Dic67 | — | 4 | 1 | no | — |
| 148 | D268 | — | 4 | 1 | no | — |
| 149 | D268 | — | 4 | 1 | no | — |
| 150 | D268 | — | 4 | 1 | no | — |
| 151 | D268 | — | 4 | 1 | no | — |
| 152 | D268 | — | 8 | 2 | no | — |
| 153 | D268 | — | 8 | 4 | no | — |
| 154 | D268 | — | 8 | 2 | no | — |
| 155 | C4×D67 | — | 4 | 1 | no | — |
| 156 | C4×D67 | — | 4 | 1 | no | — |
| 157 | C4×D67 | — | 8 | 1 | no | — |
| 158 | C4×D67 | — | 8 | 2 | no | — |
| 159 | C4×D67 | — | 8 | 1 | no | — |
| 160 | C4×D67 | — | 8 | 1 | no | — |
| 161 | Dic134 | — | 4 | 1 | no | — |
| 162 | Dic134 | — | 4 | 1 | no | — |
| 163 | C8×C67 | — | 2 | 1 | no | — |
| 164 | C8×C67 | — | 2 | 1 | no | — |
| 165 | C67⋊C8 | — | 4 | 1 | no | — |
| 166 | C22×C67 | — | 2 | 1 | no | — |
| 167 | C22×C67 | — | 4 | 1 | no | — |
| 168 | C22×C67 | #447 | 1 | 1 | yes | characteristic |
| 169 | C2×D67 | — | 4 | 1 | no | — |
| 170 | C2×D67 | — | 4 | 1 | no | — |
| 171 | C2×D67 | — | 4 | 2 | no | — |
| 172 | C2×D67 | — | 4 | 1 | no | — |
| 173 | C2×D67 | — | 8 | 1 | no | — |
| 174 | C2×D67 | — | 8 | 1 | no | — |
| 175 | C2×D67 | — | 8 | 1 | no | — |
| 176 | C2×D67 | — | 8 | 2 | no | — |
| 177 | C2×D67 | — | 8 | 1 | no | — |
| 178 | C2×D67 | — | 8 | 1 | no | — |
| 179 | C4×C67 | — | 2 | 1 | no | — |
| 180 | C4×C67 | — | 8 | 1 | no | — |
| 181 | C4×C67 | — | 8 | 2 | no | — |
| 182 | C4×C67 | — | 8 | 1 | no | — |
| 183 | C4×C67 | #453 | 1 | 1 | yes | characteristic |
| 184 | C4×C67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 185 | Dic67 | — | 4 | 1 | no | — |
| 186 | Dic67 | — | 8 | 1 | no | — |
| 187 | Dic67 | — | 8 | 1 | no | — |
| 188 | #12116 | — | 67 | 1 | no | maximal, Sylow |
| 189 | C2×C67 | — | 2 | 1 | no | — |
| 190 | C2×C67 | — | 4 | 1 | no | — |
| 191 | C2×C67 | #1595 | 1 | 1 | yes | characteristic |
| 192 | D67 | — | 8 | 1 | no | — |
| 193 | D67 | — | 16 | 1 | no | — |
| 194 | D67 | — | 16 | 1 | no | — |
| 195 | #3197 | — | 67 | 1 | no | — |
| 196 | #2191 | — | 67 | 1 | no | — |
| 197 | #2190 | — | 67 | 1 | no | — |
| 198 | #2010 | — | 67 | 1 | no | — |
| 199 | #1340 | D67 | 1 | 1 | yes | characteristic, complemented |
| 200 | #1339 | — | 67 | 1 | no | — |
| 201 | #1320 | — | 67 | 1 | no | — |
| 202 | C67 | #12116 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 203 | #575 | — | 67 | 1 | no | — |
| 204 | #525 | — | 134 | 1 | no | — |
| 205 | #525 | — | 134 | 1 | no | — |
| 206 | #510 | — | 134 | 1 | no | — |
| 207 | #509 | — | 134 | 1 | no | — |
| 208 | #485 | — | 134 | 1 | no | — |
| 209 | #482 | — | 134 | 1 | no | — |
| 210 | #470 | C2×D67 | 1 | 1 | yes | characteristic |
| 211 | #469 | — | 67 | 1 | no | — |
| 212 | #468 | — | 134 | 1 | no | — |
| 213 | #452 | — | 134 | 1 | no | — |
| 214 | #449 | — | 134 | 1 | no | — |
| 215 | #421 | — | 134 | 1 | no | — |
| 216 | #407 | — | 67 | 1 | no | — |
| 217 | #360 | — | 134 | 1 | no | — |
| 218 | #360 | — | 134 | 1 | no | — |
| 219 | #349 | — | 67 | 1 | no | — |
| 220 | #349 | C2×D67 | 1 | 1 | yes | characteristic |
| 221 | H(3,ℤ/4) | C2×D67 | 1 | 1 | yes | characteristic |
| 222 | C2×#41 | — | 134 | 1 | no | — |
| 223 | C2×#41 | — | 134 | 1 | no | — |
| 224 | C23×C4 | — | 67 | 1 | no | — |
| 225 | #137 | — | 268 | 1 | no | — |
| 226 | AGL(1,ℤ/8) | — | 268 | 1 | no | — |
| 227 | #135 | — | 134 | 1 | no | — |
| 228 | #135 | — | 134 | 1 | no | — |
| 229 | C2×Q16 | D268 | 1 | 1 | yes | characteristic, complemented |
| 230 | C2×SD16 | — | 134 | 1 | no | — |
| 231 | C2×D8 | — | 67 | 1 | no | — |
| 232 | C2×M16 | — | 67 | 1 | no | — |
| 233 | C2×M16 | C22×D67 | 1 | 1 | yes | characteristic |
| 234 | #123 | — | 268 | 1 | no | — |
| 235 | #123 | — | 268 | 1 | no | — |
| 236 | C22⋊Q8 | — | 2 | 1 | no | — |
| 237 | C22⋊Q8 | — | 268 | 1 | no | — |
| 238 | C22⋊Q8 | — | 134 | 1 | no | — |
| 239 | #121 | — | 268 | 1 | no | — |
| 240 | #121 | — | 134 | 1 | no | — |
| 241 | #121 | — | 134 | 1 | no | — |
| 242 | #120 | — | 268 | 1 | no | — |
| 243 | #120 | — | 268 | 1 | no | — |
| 244 | C4×D4 | — | 268 | 2 | no | — |
| 245 | C4×D4 | — | 268 | 1 | no | — |
| 246 | C4×D4 | — | 268 | 1 | no | — |
| 247 | #117 | — | 2 | 1 | no | — |
| 248 | #117 | — | 134 | 1 | no | — |
| 249 | Q32 | — | 268 | 1 | no | — |
| 250 | SD32 | — | 268 | 1 | no | — |
| 251 | SD32 | — | 268 | 1 | no | — |
| 252 | D16 | — | 268 | 1 | no | — |
| 253 | M32 | — | 2 | 1 | no | — |
| 254 | M32 | — | 134 | 1 | no | — |
| 255 | #107 | — | 134 | 1 | no | — |
| 256 | #106 | — | 67 | 1 | no | — |
| 257 | #106 | D268 | 1 | 1 | yes | characteristic, complemented |
| 258 | #104 | — | 268 | 2 | no | — |
| 259 | #103 | — | 2 | 1 | no | — |
| 260 | #103 | — | 134 | 1 | no | — |
| 261 | #102 | — | 134 | 1 | no | — |
| 262 | #102 | — | 134 | 1 | no | — |
| 263 | C22⋊C8 | — | 134 | 1 | no | — |
| 264 | C22⋊C8 | — | 134 | 1 | no | — |
| 265 | C24 | — | 67 | 1 | no | — |
| 266 | #41 | — | 268 | 1 | no | — |
| 267 | #41 | — | 268 | 1 | no | — |
| 268 | #41 | — | 268 | 1 | no | — |
| 269 | #41 | — | 268 | 1 | no | — |
| 270 | #41 | — | 536 | 1 | no | — |
| 271 | #41 | — | 536 | 1 | no | — |
| 272 | C2×Q8 | — | 2 | 1 | no | — |
| 273 | C2×Q8 | — | 134 | 1 | no | — |
| 274 | C2×D4 | — | 268 | 2 | no | — |
| 275 | C2×D4 | — | 268 | 1 | no | — |
| 276 | C2×D4 | — | 268 | 1 | no | — |
| 277 | C2×D4 | — | 268 | 1 | no | — |
| 278 | C2×D4 | — | 268 | 1 | no | — |
| 279 | C2×D4 | — | 134 | 1 | no | — |
| 280 | C2×D4 | — | 134 | 1 | no | — |
| 281 | C22×C4 | — | 268 | 1 | no | — |
| 282 | C22×C4 | — | 268 | 1 | no | — |
| 283 | C22×C4 | — | 268 | 1 | no | — |
| 284 | C22×C4 | — | 268 | 1 | no | — |
| 285 | C22×C4 | — | 67 | 1 | no | — |
| 286 | C22×C4 | — | 134 | 1 | no | — |
| 287 | C22×C4 | — | 134 | 1 | no | — |
| 288 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 289 | Q16 | — | 4 | 1 | no | — |
| 290 | Q16 | — | 134 | 1 | no | — |
| 291 | Q16 | — | 134 | 1 | no | — |
| 292 | SD16 | — | 268 | 1 | no | — |
| 293 | SD16 | — | 268 | 1 | no | — |
| 294 | SD16 | — | 536 | 1 | no | — |
| 295 | D8 | — | 268 | 1 | no | — |
| 296 | D8 | — | 134 | 1 | no | — |
| 297 | D8 | — | 134 | 1 | no | — |
| 298 | M16 | — | 4 | 1 | no | — |
| 299 | M16 | — | 268 | 1 | no | — |
| 300 | C2×C8 | — | 134 | 1 | no | — |
| 301 | C2×C8 | D4×D67 | 1 | 1 | yes | characteristic |
| 302 | C2×C8 | C2×D268 | 1 | 1 | yes | characteristic |
| 303 | C4⋊C4 | — | 2 | 1 | no | — |
| 304 | C4⋊C4 | — | 4 | 1 | no | — |
| 305 | C4⋊C4 | — | 4 | 1 | no | — |
| 306 | C4⋊C4 | — | 268 | 2 | no | — |
| 307 | C4⋊C4 | — | 268 | 1 | no | — |
| 308 | C4⋊C4 | — | 134 | 1 | no | — |
| 309 | C22⋊C4 | — | 4 | 1 | no | — |
| 310 | C22⋊C4 | — | 4 | 1 | no | — |
| 311 | C22⋊C4 | — | 268 | 2 | no | — |
| 312 | C22⋊C4 | — | 268 | 2 | no | — |
| 313 | C22⋊C4 | — | 268 | 1 | no | — |
| 314 | C22⋊C4 | — | 268 | 1 | no | — |
| 315 | C22⋊C4 | — | 268 | 1 | no | — |
| 316 | C22⋊C4 | — | 268 | 1 | no | — |
| 317 | C42 | — | 2 | 2 | no | — |
| 318 | C42 | — | 268 | 1 | no | — |
| 319 | C16 | — | 4 | 1 | no | — |
| 320 | C16 | — | 268 | 1 | no | — |
| 321 | C23 | — | 268 | 1 | no | — |
| 322 | C23 | — | 268 | 1 | no | — |
| 323 | C23 | — | 268 | 1 | no | — |
| 324 | C23 | — | 536 | 1 | no | — |
| 325 | C23 | — | 134 | 1 | no | — |
| 326 | C23 | D8×D67 | 1 | 1 | yes | characteristic |
| 327 | Q8 | — | 4 | 1 | no | — |
| 328 | Q8 | — | 4 | 1 | no | — |
| 329 | Q8 | — | 268 | 1 | no | — |
| 330 | Q8 | — | 268 | 1 | no | — |
| 331 | D4 | — | 268 | 1 | no | — |
| 332 | D4 | — | 268 | 1 | no | — |
| 333 | D4 | — | 268 | 1 | no | — |
| 334 | D4 | — | 268 | 1 | no | — |
| 335 | D4 | — | 536 | 2 | no | — |
| 336 | D4 | — | 536 | 2 | no | — |
| 337 | D4 | — | 536 | 4 | no | — |
| 338 | D4 | — | 536 | 1 | no | — |
| 339 | D4 | — | 536 | 2 | no | — |
| 340 | D4 | — | 536 | 1 | no | — |
| 341 | C2×C4 | — | 2 | 1 | no | — |
| 342 | C2×C4 | — | 2 | 1 | no | — |
| 343 | C2×C4 | — | 4 | 2 | no | — |
| 344 | C2×C4 | — | 4 | 1 | no | — |
| 345 | C2×C4 | — | 4 | 1 | no | — |
| 346 | C2×C4 | — | 268 | 1 | no | — |
| 347 | C2×C4 | — | 268 | 1 | no | — |
| 348 | C2×C4 | — | 268 | 1 | no | — |
| 349 | C2×C4 | — | 268 | 1 | no | — |
| 350 | C2×C4 | — | 268 | 1 | no | — |
| 351 | C2×C4 | — | 536 | 1 | no | — |
| 352 | C2×C4 | — | 536 | 1 | no | — |
| 353 | C2×C4 | — | 536 | 2 | no | — |
| 354 | C2×C4 | — | 536 | 1 | no | — |
| 355 | C2×C4 | — | 134 | 1 | no | — |
| 356 | C2×C4 | #14524013 | 1 | 1 | yes | characteristic |
| 357 | C2×C4 | #14524070 | 1 | 1 | yes | characteristic |
| 358 | C8 | — | 2 | 1 | no | — |
| 359 | C8 | — | 2 | 1 | no | — |
| 360 | C8 | — | 268 | 1 | no | — |
| 361 | C22 | — | 2 | 1 | no | — |
| 362 | C22 | — | 4 | 1 | no | — |
| 363 | C22 | — | 268 | 1 | no | — |
| 364 | C22 | — | 268 | 1 | no | — |
| 365 | C22 | — | 268 | 2 | no | — |
| 366 | C22 | — | 268 | 1 | no | — |
| 367 | C22 | — | 536 | 1 | no | — |
| 368 | C22 | — | 536 | 1 | no | — |
| 369 | C22 | — | 536 | 1 | no | — |
| 370 | C22 | — | 536 | 2 | no | — |
| 371 | C22 | — | 536 | 1 | no | — |
| 372 | C22 | — | 536 | 1 | no | — |
| 373 | C22 | #16863531 | 1 | 1 | yes | characteristic |
| 374 | C4 | — | 2 | 1 | no | — |
| 375 | C4 | — | 8 | 1 | no | — |
| 376 | C4 | — | 8 | 2 | no | — |
| 377 | C4 | — | 8 | 1 | no | — |
| 378 | C4 | — | 268 | 1 | no | — |
| 379 | C4 | — | 536 | 1 | no | — |
| 380 | C4 | — | 536 | 1 | no | — |
| 381 | C4 | #16863565 | 1 | 1 | yes | characteristic |
| 382 | C4 | #16863584 | 1 | 1 | yes | characteristic |
| 383 | C2 | — | 2 | 1 | no | — |
| 384 | C2 | — | 4 | 1 | no | — |
| 385 | C2 | — | 536 | 1 | no | — |
| 386 | C2 | — | 1072 | 1 | no | — |
| 387 | C2 | — | 1072 | 1 | no | — |
| 388 | C2 | #22559128 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22571052 | C2 | semidirect |
| 2. #22562159 | C2 | semidirect |
| 3. #22562157 | C2 | semidirect |
| 4. #22561277 | C2 | semidirect |
| 5. #22558193 | C2 | semidirect |
| 6. #22558144 | C2 | semidirect |
| 7. C67×#1340 | C2 | semidirect |
| 35. C2×D536 | D4 | semidirect |
| 56. #14523975 | D4 | semidirect |
| 63. C2×Q16×C67 | D4 | semidirect |
| 68. #106×C67 | D4 | semidirect |
| 199. #1340 | D67 | semidirect |
| 202. C67 | #12116 | semidirect |
| 229. C2×Q16 | D268 | semidirect |
| 257. #106 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571052 | 2 |
| #22562159 | 2 |
| #22562157 | 2 |
| #22561277 | 2 |
| #22558193 | 2 |
| #22558144 | 2 |
| C67×#1340 | 2 |
| #12116 | 67 |