Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
578 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 81 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 | #22571206 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22571198 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22570675 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22558677 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22558627 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22558562 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C67×#1291 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14524076 | — | 2 | 1 | no | — |
| 9 | C2×#14524071 | — | 2 | 1 | no | — |
| 10 | #16863946 | C22 | 1 | 1 | yes | characteristic |
| 11 | #16863946 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#14524031 | C22 | 1 | 1 | yes | characteristic |
| 13 | #16863790 | — | 2 | 1 | no | — |
| 14 | #16863785 | — | 2 | 1 | no | — |
| 15 | #16863785 | — | 2 | 1 | no | — |
| 16 | #16863785 | — | 2 | 1 | no | — |
| 17 | #16863780 | — | 2 | 2 | no | — |
| 18 | #16863756 | — | 2 | 1 | no | — |
| 19 | #16863756 | — | 2 | 1 | no | — |
| 20 | #16863612 | — | 2 | 2 | no | — |
| 21 | #16863602 | — | 2 | 1 | no | — |
| 22 | #16863592 | — | 2 | 1 | no | — |
| 23 | #16863543 | — | 2 | 2 | no | — |
| 24 | #16863537 | — | 2 | 1 | no | — |
| 25 | #16863532 | — | 2 | 1 | no | — |
| 26 | #16863449 | C22 | 1 | 1 | yes | characteristic |
| 27 | #16863125 | — | 2 | 2 | no | — |
| 28 | #16863123 | — | 2 | 2 | no | — |
| 29 | #16863119 | — | 2 | 2 | no | — |
| 30 | #432×C67 | C22 | 1 | 1 | yes | characteristic |
| 31 | #432×C67 | C22 | 1 | 1 | yes | characteristic |
| 32 | C4×M16×C67 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#11761628 | — | 2 | 1 | no | — |
| 34 | C2×#11761628 | — | 2 | 1 | no | — |
| 35 | C22×Dic134 | D4 | 1 | 1 | yes | characteristic |
| 36 | C22×D268 | D4 | 1 | 1 | yes | characteristic |
| 37 | #14524076 | — | 4 | 4 | no | — |
| 38 | #14524071 | — | 4 | 4 | no | — |
| 39 | C2×Dic268 | — | 2 | 2 | no | — |
| 40 | C2×#11761617 | — | 2 | 2 | no | — |
| 41 | C2×#11761617 | — | 2 | 2 | no | — |
| 42 | C2×#11761617 | — | 2 | 2 | no | — |
| 43 | C2×#11761617 | — | 2 | 2 | no | — |
| 44 | C2×D536 | — | 2 | 2 | no | — |
| 45 | C2×D536 | — | 2 | 2 | no | — |
| 46 | C2×D536 | — | 2 | 2 | no | — |
| 47 | #14524043 | D4 | 1 | 1 | yes | characteristic |
| 48 | #14524043 | D4 | 1 | 1 | yes | characteristic |
| 49 | #14524040 | D4 | 1 | 1 | yes | characteristic |
| 50 | #14524040 | D4 | 1 | 1 | yes | characteristic |
| 51 | #14524031 | — | 2 | 1 | no | — |
| 52 | #14524031 | — | 2 | 1 | no | — |
| 53 | #14524031 | — | 2 | 1 | no | — |
| 54 | #14524031 | — | 2 | 1 | no | — |
| 55 | #14524031 | — | 2 | 1 | no | — |
| 56 | #14524031 | — | 2 | 1 | no | — |
| 57 | #14524017 | — | 2 | 1 | no | — |
| 58 | #14524017 | — | 2 | 1 | no | — |
| 59 | #14524017 | — | 2 | 1 | no | — |
| 60 | #14524017 | — | 2 | 1 | no | — |
| 61 | C4×D268 | — | 2 | 1 | no | — |
| 62 | C4×D268 | — | 2 | 1 | no | — |
| 63 | C4×D268 | — | 2 | 1 | no | — |
| 64 | C4×D268 | — | 2 | 1 | no | — |
| 65 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 66 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 67 | C4⋊(C67⋊C8) | — | 2 | 1 | no | — |
| 68 | #14523968 | — | 2 | 2 | no | — |
| 69 | #14523968 | — | 2 | 2 | no | — |
| 70 | #14523965 | — | 2 | 2 | no | — |
| 71 | #14523965 | — | 2 | 2 | no | — |
| 72 | C22⋊(C67⋊C8) | — | 2 | 1 | no | — |
| 73 | C4×C67⋊C8 | — | 2 | 1 | no | — |
| 74 | C2×M16×C67 | — | 2 | 1 | no | — |
| 75 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 76 | C4⋊C8×C67 | — | 2 | 1 | no | — |
| 77 | C4⋊C8×C67 | D4 | 1 | 2 | yes | — |
| 78 | C22⋊C8×C67 | — | 2 | 1 | no | — |
| 79 | C22⋊C8×C67 | D4 | 1 | 2 | yes | — |
| 80 | #97×C67 | — | 2 | 1 | no | — |
| 81 | #97×C67 | — | 2 | 1 | no | — |
| 82 | #97×C67 | — | 2 | 1 | no | — |
| 83 | C4×C8×C67 | D4 | 1 | 2 | yes | — |
| 84 | C23×D67 | — | 2 | 1 | no | — |
| 85 | #11761628 | — | 4 | 2 | no | — |
| 86 | #11761628 | — | 4 | 2 | no | — |
| 87 | #11761628 | — | 8 | 2 | no | — |
| 88 | C2×Dic134 | — | 2 | 1 | no | — |
| 89 | C2×Dic134 | — | 2 | 1 | no | — |
| 90 | C2×Dic134 | — | 2 | 1 | no | — |
| 91 | C2×Dic134 | — | 2 | 1 | no | — |
| 92 | C2×Dic134 | — | 4 | 2 | no | — |
| 93 | C2×D268 | — | 2 | 1 | no | — |
| 94 | C2×D268 | — | 2 | 1 | no | — |
| 95 | C2×D268 | — | 2 | 1 | no | — |
| 96 | C2×D268 | — | 2 | 1 | no | — |
| 97 | C2×D268 | — | 2 | 1 | no | — |
| 98 | C2×D268 | — | 2 | 1 | no | — |
| 99 | C2×D268 | — | 2 | 1 | no | — |
| 100 | C2×D268 | — | 2 | 1 | no | — |
| 101 | C2×D268 | — | 4 | 2 | no | — |
| 102 | C2×C22⋊D67 | — | 4 | 1 | no | — |
| 103 | C2×C22⋊D67 | — | 4 | 1 | no | — |
| 104 | C22×Dic67 | — | 2 | 1 | no | — |
| 105 | C2×C4×D67 | — | 4 | 1 | no | — |
| 106 | C2×C4×D67 | — | 4 | 1 | no | — |
| 107 | Dic268 | — | 4 | 4 | no | — |
| 108 | #11761617 | — | 4 | 4 | no | — |
| 109 | #11761617 | — | 4 | 4 | no | — |
| 110 | #11761617 | — | 8 | 2 | no | — |
| 111 | #11761617 | — | 8 | 2 | no | — |
| 112 | D536 | — | 4 | 4 | no | — |
| 113 | D536 | — | 8 | 2 | no | — |
| 114 | D536 | — | 8 | 2 | no | — |
| 115 | C2×C67⋊C8 | — | 4 | 1 | no | — |
| 116 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 117 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 118 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 119 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 120 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 121 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 122 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 123 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 124 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 125 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 126 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 127 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 128 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C22×C4×C67 | #41 | 1 | 1 | yes | characteristic |
| 131 | M16×C67 | — | 2 | 4 | no | — |
| 132 | C2×C8×C67 | — | 2 | 2 | no | — |
| 133 | C2×C8×C67 | — | 2 | 2 | no | — |
| 134 | C2×C8×C67 | — | 2 | 2 | no | — |
| 135 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C23×C67 | #121 | 1 | 1 | yes | characteristic |
| 140 | C22×D67 | — | 4 | 1 | no | — |
| 141 | C22×D67 | — | 4 | 1 | no | — |
| 142 | C22×D67 | — | 4 | 1 | no | — |
| 143 | C22×D67 | — | 4 | 2 | no | — |
| 144 | C22×D67 | — | 8 | 1 | no | — |
| 145 | C22×D67 | — | 8 | 1 | no | — |
| 146 | C2×C4×C67 | — | 2 | 2 | no | — |
| 147 | C2×C4×C67 | — | 4 | 1 | no | — |
| 148 | C2×C4×C67 | — | 4 | 1 | no | — |
| 149 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 150 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 151 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 152 | C2×C4×C67 | #121 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×C67 | #121 | 1 | 1 | yes | characteristic |
| 154 | C2×C4×C67 | #127 | 1 | 1 | yes | characteristic |
| 155 | C22⋊D67 | — | 8 | 2 | no | — |
| 156 | C22⋊D67 | — | 8 | 2 | no | — |
| 157 | C2×Dic67 | — | 4 | 1 | no | — |
| 158 | C2×Dic67 | — | 4 | 1 | no | — |
| 159 | C2×Dic67 | — | 4 | 1 | no | — |
| 160 | C2×Dic67 | — | 8 | 1 | no | — |
| 161 | D268 | — | 4 | 1 | no | — |
| 162 | D268 | — | 4 | 2 | no | — |
| 163 | D268 | — | 4 | 1 | no | — |
| 164 | D268 | — | 4 | 2 | no | — |
| 165 | D268 | — | 4 | 1 | no | — |
| 166 | D268 | — | 4 | 1 | no | — |
| 167 | D268 | — | 4 | 2 | no | — |
| 168 | D268 | — | 4 | 2 | no | — |
| 169 | D268 | — | 4 | 2 | no | — |
| 170 | D268 | — | 4 | 2 | no | — |
| 171 | C4×D67 | — | 8 | 2 | no | — |
| 172 | C4×D67 | — | 8 | 2 | no | — |
| 173 | Dic134 | — | 4 | 1 | no | — |
| 174 | Dic134 | — | 4 | 2 | no | — |
| 175 | Dic134 | — | 4 | 2 | no | — |
| 176 | Dic134 | — | 4 | 1 | no | — |
| 177 | Dic134 | — | 4 | 2 | no | — |
| 178 | C8×C67 | — | 2 | 4 | no | — |
| 179 | C8×C67 | — | 4 | 2 | no | — |
| 180 | C8×C67 | — | 4 | 2 | no | — |
| 181 | C67⋊C8 | — | 8 | 1 | no | — |
| 182 | C22×C67 | — | 2 | 1 | no | — |
| 183 | C22×C67 | — | 2 | 1 | no | — |
| 184 | C22×C67 | — | 2 | 1 | no | — |
| 185 | C22×C67 | #392 | 1 | 1 | yes | characteristic |
| 186 | C2×D67 | — | 8 | 1 | no | — |
| 187 | C2×D67 | — | 8 | 1 | no | — |
| 188 | C2×D67 | — | 8 | 1 | no | — |
| 189 | C2×D67 | — | 8 | 1 | no | — |
| 190 | C2×D67 | — | 8 | 1 | no | — |
| 191 | C2×D67 | — | 8 | 1 | no | — |
| 192 | C2×D67 | — | 8 | 1 | no | — |
| 193 | C2×D67 | — | 8 | 1 | no | — |
| 194 | C2×D67 | — | 8 | 1 | no | — |
| 195 | C2×D67 | — | 16 | 2 | no | — |
| 196 | C4×C67 | — | 2 | 1 | no | — |
| 197 | C4×C67 | — | 2 | 1 | no | — |
| 198 | C4×C67 | — | 2 | 1 | no | — |
| 199 | C4×C67 | — | 2 | 1 | no | — |
| 200 | C4×C67 | — | 2 | 1 | no | — |
| 201 | C4×C67 | #453 | 1 | 2 | yes | — |
| 202 | Dic67 | — | 8 | 1 | no | — |
| 203 | Dic67 | — | 8 | 1 | no | — |
| 204 | Dic67 | — | 8 | 1 | no | — |
| 205 | #10120 | — | 67 | 1 | no | maximal, Sylow |
| 206 | C2×C67 | — | 4 | 1 | no | — |
| 207 | C2×C67 | #2002 | 1 | 1 | yes | characteristic |
| 208 | C2×C67 | #2008 | 1 | 1 | yes | characteristic |
| 209 | C2×C67 | #2017 | 1 | 1 | yes | characteristic |
| 210 | D67 | — | 16 | 1 | no | — |
| 211 | D67 | — | 16 | 1 | no | — |
| 212 | D67 | — | 16 | 1 | no | — |
| 213 | #3214 | — | 67 | 1 | no | — |
| 214 | #3213 | — | 67 | 1 | no | — |
| 215 | #3153 | — | 67 | 1 | no | — |
| 216 | #1496 | — | 67 | 1 | no | — |
| 217 | #1484 | — | 67 | 1 | no | — |
| 218 | #1469 | — | 67 | 1 | no | — |
| 219 | #1291 | D67 | 1 | 1 | yes | characteristic, complemented |
| 220 | C67 | #10120 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 221 | C2×#137 | — | 134 | 1 | no | — |
| 222 | C2×AGL(1,ℤ/8) | — | 134 | 1 | no | — |
| 223 | #532 | — | 67 | 1 | no | — |
| 224 | #532 | — | 67 | 1 | no | — |
| 225 | C2×#124 | — | 67 | 1 | no | — |
| 226 | #497 | — | 134 | 1 | no | — |
| 227 | #496 | — | 134 | 1 | no | — |
| 228 | #496 | — | 134 | 1 | no | — |
| 229 | #496 | — | 134 | 1 | no | — |
| 230 | #495 | — | 134 | 2 | no | — |
| 231 | #489 | — | 134 | 1 | no | — |
| 232 | #489 | — | 134 | 1 | no | — |
| 233 | #463 | — | 134 | 2 | no | — |
| 234 | #461 | — | 134 | 1 | no | — |
| 235 | #459 | — | 134 | 1 | no | — |
| 236 | #449 | — | 134 | 2 | no | — |
| 237 | #448 | — | 134 | 1 | no | — |
| 238 | #447 | — | 134 | 1 | no | — |
| 239 | #432 | C2×D67 | 1 | 1 | yes | characteristic |
| 240 | #432 | C2×D67 | 1 | 1 | yes | characteristic |
| 241 | #431 | — | 67 | 1 | no | — |
| 242 | C4×M16 | C2×D67 | 1 | 1 | yes | characteristic |
| 243 | D4⋊C8 | — | 134 | 2 | no | — |
| 244 | D4⋊C8 | — | 134 | 2 | no | — |
| 245 | #323 | — | 134 | 2 | no | — |
| 246 | C2×#41 | — | 134 | 1 | no | — |
| 247 | C2×#41 | — | 134 | 1 | no | — |
| 248 | C22×Q8 | — | 67 | 1 | no | — |
| 249 | C22×D4 | — | 67 | 1 | no | — |
| 250 | #137 | — | 268 | 4 | no | — |
| 251 | AGL(1,ℤ/8) | — | 268 | 4 | no | — |
| 252 | C2×Q16 | — | 134 | 2 | no | — |
| 253 | C2×SD16 | — | 134 | 2 | no | — |
| 254 | C2×SD16 | — | 134 | 2 | no | — |
| 255 | C2×SD16 | — | 134 | 2 | no | — |
| 256 | C2×SD16 | — | 134 | 2 | no | — |
| 257 | C2×D8 | — | 134 | 2 | no | — |
| 258 | C2×D8 | — | 134 | 2 | no | — |
| 259 | C2×D8 | — | 134 | 2 | no | — |
| 260 | C2×M16 | — | 2 | 1 | no | — |
| 261 | C4⋊Q8 | — | 67 | 1 | no | — |
| 262 | C4⋊Q8 | — | 67 | 1 | no | — |
| 263 | #127 | — | 67 | 1 | no | — |
| 264 | #127 | — | 67 | 1 | no | — |
| 265 | #124 | — | 134 | 1 | no | — |
| 266 | #124 | — | 134 | 1 | no | — |
| 267 | #124 | — | 134 | 1 | no | — |
| 268 | #124 | — | 134 | 1 | no | — |
| 269 | #124 | — | 134 | 1 | no | — |
| 270 | #124 | — | 134 | 1 | no | — |
| 271 | #121 | — | 134 | 1 | no | — |
| 272 | #121 | — | 134 | 1 | no | — |
| 273 | #121 | — | 134 | 1 | no | — |
| 274 | #121 | — | 134 | 1 | no | — |
| 275 | C4×D4 | — | 134 | 1 | no | — |
| 276 | C4×D4 | — | 134 | 1 | no | — |
| 277 | C4×D4 | — | 134 | 1 | no | — |
| 278 | C4×D4 | — | 134 | 1 | no | — |
| 279 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 280 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 281 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 282 | C4⋊C8 | — | 2 | 1 | no | — |
| 283 | C4⋊C8 | — | 134 | 1 | no | — |
| 284 | C4⋊C8 | D268 | 1 | 2 | yes | — |
| 285 | #103 | — | 134 | 2 | no | — |
| 286 | #103 | — | 134 | 2 | no | — |
| 287 | #102 | — | 134 | 2 | no | — |
| 288 | #102 | — | 134 | 2 | no | — |
| 289 | C22⋊C8 | — | 2 | 1 | no | — |
| 290 | C22⋊C8 | — | 134 | 1 | no | — |
| 291 | C22⋊C8 | D268 | 1 | 2 | yes | — |
| 292 | #97 | — | 2 | 1 | no | — |
| 293 | #97 | — | 2 | 1 | no | — |
| 294 | #97 | — | 2 | 1 | no | — |
| 295 | C4×C8 | — | 134 | 1 | no | — |
| 296 | C4×C8 | D268 | 1 | 2 | yes | — |
| 297 | C24 | — | 134 | 1 | no | — |
| 298 | #41 | — | 268 | 2 | no | — |
| 299 | #41 | — | 268 | 2 | no | — |
| 300 | #41 | — | 536 | 2 | no | — |
| 301 | C2×Q8 | — | 268 | 2 | no | — |
| 302 | C2×Q8 | — | 134 | 1 | no | — |
| 303 | C2×Q8 | — | 134 | 1 | no | — |
| 304 | C2×Q8 | — | 134 | 1 | no | — |
| 305 | C2×Q8 | — | 134 | 1 | no | — |
| 306 | C2×D4 | — | 268 | 2 | no | — |
| 307 | C2×D4 | — | 268 | 1 | no | — |
| 308 | C2×D4 | — | 268 | 1 | no | — |
| 309 | C2×D4 | — | 134 | 1 | no | — |
| 310 | C2×D4 | — | 134 | 1 | no | — |
| 311 | C2×D4 | — | 134 | 1 | no | — |
| 312 | C2×D4 | — | 134 | 1 | no | — |
| 313 | C2×D4 | — | 134 | 1 | no | — |
| 314 | C2×D4 | — | 134 | 1 | no | — |
| 315 | C2×D4 | — | 134 | 1 | no | — |
| 316 | C2×D4 | — | 134 | 1 | no | — |
| 317 | C22×C4 | — | 268 | 1 | no | — |
| 318 | C22×C4 | — | 268 | 1 | no | — |
| 319 | C22×C4 | — | 134 | 1 | no | — |
| 320 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 321 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 322 | C22×C4 | #11761629 | 1 | 1 | yes | characteristic |
| 323 | Q16 | — | 268 | 4 | no | — |
| 324 | SD16 | — | 268 | 4 | no | — |
| 325 | SD16 | — | 268 | 4 | no | — |
| 326 | SD16 | — | 536 | 2 | no | — |
| 327 | SD16 | — | 536 | 2 | no | — |
| 328 | D8 | — | 268 | 4 | no | — |
| 329 | D8 | — | 536 | 2 | no | — |
| 330 | D8 | — | 536 | 2 | no | — |
| 331 | M16 | — | 2 | 4 | no | — |
| 332 | C2×C8 | — | 2 | 2 | no | — |
| 333 | C2×C8 | — | 2 | 2 | no | — |
| 334 | C2×C8 | — | 2 | 2 | no | — |
| 335 | C2×C8 | — | 268 | 1 | no | — |
| 336 | C4⋊C4 | — | 134 | 1 | no | — |
| 337 | C4⋊C4 | — | 134 | 1 | no | — |
| 338 | C4⋊C4 | — | 134 | 1 | no | — |
| 339 | C4⋊C4 | — | 134 | 1 | no | — |
| 340 | C22⋊C4 | — | 268 | 1 | no | — |
| 341 | C22⋊C4 | — | 268 | 1 | no | — |
| 342 | C22⋊C4 | — | 268 | 1 | no | — |
| 343 | C22⋊C4 | — | 268 | 1 | no | — |
| 344 | C22⋊C4 | — | 268 | 1 | no | — |
| 345 | C22⋊C4 | — | 268 | 1 | no | — |
| 346 | C22⋊C4 | — | 268 | 1 | no | — |
| 347 | C22⋊C4 | — | 268 | 1 | no | — |
| 348 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 349 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 350 | C42 | C2×D268 | 1 | 1 | yes | characteristic |
| 351 | C42 | C2×D268 | 1 | 1 | yes | characteristic |
| 352 | C23 | — | 268 | 2 | no | — |
| 353 | C23 | — | 268 | 1 | no | — |
| 354 | C23 | — | 268 | 1 | no | — |
| 355 | C23 | — | 268 | 1 | no | — |
| 356 | C23 | — | 536 | 1 | no | — |
| 357 | C23 | — | 536 | 1 | no | — |
| 358 | C23 | #14524018 | 1 | 1 | yes | characteristic |
| 359 | Q8 | — | 268 | 1 | no | — |
| 360 | Q8 | — | 268 | 2 | no | — |
| 361 | Q8 | — | 268 | 2 | no | — |
| 362 | Q8 | — | 268 | 1 | no | — |
| 363 | Q8 | — | 268 | 2 | no | — |
| 364 | D4 | — | 268 | 1 | no | — |
| 365 | D4 | — | 268 | 2 | no | — |
| 366 | D4 | — | 268 | 1 | no | — |
| 367 | D4 | — | 268 | 2 | no | — |
| 368 | D4 | — | 268 | 1 | no | — |
| 369 | D4 | — | 268 | 1 | no | — |
| 370 | D4 | — | 268 | 2 | no | — |
| 371 | D4 | — | 268 | 2 | no | — |
| 372 | D4 | — | 268 | 2 | no | — |
| 373 | D4 | — | 268 | 2 | no | — |
| 374 | D4 | — | 536 | 2 | no | — |
| 375 | D4 | — | 536 | 2 | no | — |
| 376 | C2×C4 | — | 2 | 2 | no | — |
| 377 | C2×C4 | — | 4 | 1 | no | — |
| 378 | C2×C4 | — | 4 | 1 | no | — |
| 379 | C2×C4 | — | 268 | 1 | no | — |
| 380 | C2×C4 | — | 268 | 1 | no | — |
| 381 | C2×C4 | — | 268 | 1 | no | — |
| 382 | C2×C4 | — | 536 | 2 | no | — |
| 383 | C2×C4 | — | 536 | 2 | no | — |
| 384 | C2×C4 | — | 536 | 1 | no | — |
| 385 | C2×C4 | #14524013 | 1 | 1 | yes | characteristic |
| 386 | C2×C4 | #14524013 | 1 | 1 | yes | characteristic |
| 387 | C2×C4 | #14524013 | 1 | 1 | yes | characteristic |
| 388 | C2×C4 | #14524018 | 1 | 1 | yes | characteristic |
| 389 | C2×C4 | #14524018 | 1 | 1 | yes | characteristic |
| 390 | C2×C4 | #14524040 | 1 | 1 | yes | characteristic |
| 391 | C8 | — | 2 | 4 | no | — |
| 392 | C8 | — | 4 | 2 | no | — |
| 393 | C8 | — | 4 | 2 | no | — |
| 394 | C8 | — | 536 | 1 | no | — |
| 395 | C22 | — | 2 | 1 | no | — |
| 396 | C22 | — | 2 | 1 | no | — |
| 397 | C22 | — | 2 | 1 | no | — |
| 398 | C22 | — | 536 | 1 | no | — |
| 399 | C22 | — | 536 | 1 | no | — |
| 400 | C22 | — | 536 | 1 | no | — |
| 401 | C22 | — | 536 | 1 | no | — |
| 402 | C22 | — | 536 | 1 | no | — |
| 403 | C22 | — | 536 | 1 | no | — |
| 404 | C22 | — | 536 | 1 | no | — |
| 405 | C22 | — | 536 | 1 | no | — |
| 406 | C22 | — | 536 | 1 | no | — |
| 407 | C22 | — | 1072 | 2 | no | — |
| 408 | C22 | #16863306 | 1 | 1 | yes | characteristic |
| 409 | C4 | — | 2 | 1 | no | — |
| 410 | C4 | — | 2 | 1 | no | — |
| 411 | C4 | — | 2 | 1 | no | — |
| 412 | C4 | — | 2 | 1 | no | — |
| 413 | C4 | — | 2 | 1 | no | — |
| 414 | C4 | — | 536 | 1 | no | — |
| 415 | C4 | — | 536 | 1 | no | — |
| 416 | C4 | — | 536 | 1 | no | — |
| 417 | C4 | #16863565 | 1 | 2 | yes | — |
| 418 | C2 | — | 4 | 1 | no | — |
| 419 | C2 | — | 1072 | 1 | no | — |
| 420 | C2 | — | 1072 | 1 | no | — |
| 421 | C2 | — | 1072 | 1 | no | — |
| 422 | C2 | #22561227 | 1 | 1 | yes | characteristic |
| 423 | C2 | #22561265 | 1 | 1 | yes | characteristic |
| 424 | C2 | #22561314 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22571206 | C2 | semidirect |
| 2. #22571198 | C2 | semidirect |
| 3. #22570675 | C2 | semidirect |
| 4. #22558677 | C2 | semidirect |
| 5. #22558627 | C2 | semidirect |
| 6. #22558562 | C2 | semidirect |
| 7. C67×#1291 | C2 | semidirect |
| 219. #1291 | D67 | semidirect |
| 220. C67 | #10120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571206 | 2 |
| #22571198 | 2 |
| #22570675 | 2 |
| #22558677 | 2 |
| #22558627 | 2 |
| #22558562 | 2 |
| C67×#1291 | 2 |
| #10120 | 67 |