Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
426 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 55 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 | #22565620 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22561255 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22559214 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #22559180 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #22558240 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22558216 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C67×#1319 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14524074 | — | 2 | 1 | no | — |
| 9 | #16863977 | C22 | 1 | 1 | yes | characteristic |
| 10 | #16863710 | — | 2 | 1 | no | — |
| 11 | #16863537 | — | 2 | 1 | no | — |
| 12 | C2×#14523971 | — | 2 | 1 | no | — |
| 13 | #16863326 | C22 | 1 | 1 | yes | characteristic |
| 14 | #16863316 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16863315 | — | 2 | 1 | no | — |
| 16 | #16863300 | — | 2 | 1 | no | — |
| 17 | #16863293 | — | 2 | 1 | no | — |
| 18 | #16863278 | — | 2 | 1 | no | — |
| 19 | #16863278 | — | 2 | 1 | no | — |
| 20 | C4×Dic67⋊C4 | — | 2 | 1 | no | — |
| 21 | #16863165 | C22 | 1 | 1 | yes | characteristic |
| 22 | #16863131 | — | 2 | 1 | no | — |
| 23 | #16863131 | — | 2 | 1 | no | — |
| 24 | #391×C67 | C22 | 1 | 1 | yes | characteristic |
| 25 | #324×C67 | C22 | 1 | 1 | yes | characteristic |
| 26 | #324×C67 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#11761628 | — | 2 | 1 | no | — |
| 28 | C22×Dic134 | D4 | 1 | 1 | yes | characteristic |
| 29 | #14524074 | — | 4 | 2 | no | — |
| 30 | #14524074 | — | 4 | 2 | no | — |
| 31 | C2×#11761618 | — | 4 | 1 | no | — |
| 32 | C2×#11761617 | — | 4 | 1 | no | — |
| 33 | C2×#11761615 | — | 4 | 1 | no | — |
| 34 | C2×#11761612 | — | 2 | 1 | no | — |
| 35 | #14524023 | — | 4 | 1 | no | — |
| 36 | #14524018 | — | 4 | 1 | no | — |
| 37 | #14524017 | — | 2 | 1 | no | — |
| 38 | #14524017 | — | 2 | 1 | no | — |
| 39 | C2×C4⋊Dic67 | D4 | 1 | 1 | yes | characteristic |
| 40 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 41 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 42 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 43 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 44 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 45 | C2×C4×Dic67 | — | 2 | 1 | no | — |
| 46 | C2×C4×Dic67 | — | 2 | 1 | no | — |
| 47 | #14523977 | — | 4 | 1 | no | — |
| 48 | #14523971 | — | 4 | 2 | no | — |
| 49 | #14523968 | — | 4 | 1 | no | — |
| 50 | #14523965 | — | 4 | 1 | no | — |
| 51 | C67⋊#95 | — | 2 | 1 | no | — |
| 52 | C67⋊#95 | — | 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 | C67⋊#95 | D4 | 1 | 1 | yes | characteristic |
| 58 | C22×Q8×C67 | D4 | 1 | 1 | yes | characteristic |
| 59 | C2×C4⋊C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×C42×C67 | D4 | 1 | 1 | yes | characteristic |
| 61 | C22⋊C8×C67 | — | 2 | 1 | no | — |
| 62 | C22⋊C8×C67 | — | 2 | 1 | no | — |
| 63 | #95×C67 | — | 2 | 1 | no | — |
| 64 | #95×C67 | — | 2 | 1 | no | — |
| 65 | #11761628 | — | 4 | 1 | no | — |
| 66 | #11761628 | — | 4 | 1 | no | — |
| 67 | #11761628 | — | 4 | 1 | no | — |
| 68 | #11761628 | — | 4 | 1 | no | — |
| 69 | C2×Dic134 | — | 2 | 1 | no | — |
| 70 | C2×Dic134 | — | 4 | 1 | no | — |
| 71 | C2×Dic134 | — | 4 | 2 | no | — |
| 72 | C2×D268 | — | 2 | 1 | no | — |
| 73 | C2×D268 | — | 2 | 1 | no | — |
| 74 | C2×D268 | — | 2 | 1 | no | — |
| 75 | C2×C22⋊D67 | — | 4 | 1 | no | — |
| 76 | C22×Dic67 | — | 2 | 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 | 1 | no | — |
| 81 | #11761618 | — | 4 | 4 | no | — |
| 82 | #11761617 | — | 8 | 2 | no | — |
| 83 | #11761615 | — | 4 | 4 | no | — |
| 84 | #11761612 | — | 2 | 2 | no | — |
| 85 | #11761612 | — | 4 | 1 | no | — |
| 86 | C2×C67⋊C8 | — | 4 | 1 | no | — |
| 87 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 88 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 89 | C4⋊Dic67 | — | 4 | 1 | no | — |
| 90 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 91 | Dic67⋊C4 | — | 4 | 2 | no | — |
| 92 | Dic67⋊C4 | — | 4 | 1 | no | — |
| 93 | Dic67⋊C4 | — | 4 | 1 | no | — |
| 94 | Dic67⋊C4 | — | 8 | 1 | no | — |
| 95 | Dic67⋊C4 | — | 8 | 1 | no | — |
| 96 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 97 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 98 | C4×Dic67 | — | 4 | 2 | no | — |
| 99 | C4×Dic67 | — | 8 | 1 | no | — |
| 100 | C2×Q8×C67 | — | 2 | 1 | no | — |
| 101 | C2×Q8×C67 | — | 2 | 1 | no | — |
| 102 | C2×Q8×C67 | — | 4 | 1 | no | — |
| 103 | C2×Q8×C67 | — | 4 | 1 | no | — |
| 104 | C22×C4×C67 | — | 2 | 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 | C2×C8×C67 | — | 4 | 1 | no | — |
| 110 | C2×C8×C67 | — | 4 | 1 | no | — |
| 111 | C4⋊C4×C67 | — | 4 | 1 | no | — |
| 112 | C42×C67 | — | 4 | 1 | no | — |
| 113 | C23×C67 | #120 | 1 | 1 | yes | characteristic |
| 114 | C22×D67 | — | 4 | 1 | no | — |
| 115 | Q8×C67 | — | 4 | 2 | no | — |
| 116 | Q8×C67 | — | 8 | 1 | no | — |
| 117 | C2×C4×C67 | — | 2 | 1 | no | — |
| 118 | C2×C4×C67 | — | 2 | 1 | no | — |
| 119 | C2×C4×C67 | — | 2 | 2 | no | — |
| 120 | C2×C4×C67 | — | 2 | 1 | no | — |
| 121 | C2×C4×C67 | — | 2 | 1 | no | — |
| 122 | C2×C4×C67 | — | 4 | 1 | no | — |
| 123 | C2×C4×C67 | — | 4 | 1 | no | — |
| 124 | C2×C4×C67 | — | 4 | 1 | no | — |
| 125 | C2×C4×C67 | — | 4 | 1 | no | — |
| 126 | C2×C4×C67 | — | 4 | 1 | no | — |
| 127 | C2×C4×C67 | — | 4 | 1 | no | — |
| 128 | C2×C4×C67 | — | 4 | 1 | no | — |
| 129 | C2×C4×C67 | #135 | 1 | 1 | yes | characteristic |
| 130 | C2×C4×C67 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 131 | C22⋊D67 | — | 8 | 1 | no | — |
| 132 | C22⋊D67 | — | 8 | 1 | no | — |
| 133 | C2×Dic67 | — | 2 | 2 | no | — |
| 134 | C2×Dic67 | — | 2 | 2 | no | — |
| 135 | C2×Dic67 | — | 2 | 2 | no | — |
| 136 | C2×Dic67 | — | 4 | 1 | no | — |
| 137 | C2×Dic67 | — | 4 | 1 | no | — |
| 138 | C2×Dic67 | — | 4 | 1 | no | — |
| 139 | C2×Dic67 | — | 4 | 1 | no | — |
| 140 | C2×Dic67 | — | 4 | 1 | no | — |
| 141 | C2×Dic67 | — | 4 | 1 | no | — |
| 142 | C2×Dic67 | — | 4 | 1 | no | — |
| 143 | C2×Dic67 | — | 4 | 1 | no | — |
| 144 | C2×Dic67 | — | 4 | 1 | no | — |
| 145 | C2×Dic67 | — | 4 | 1 | no | — |
| 146 | D268 | — | 4 | 1 | no | — |
| 147 | D268 | — | 4 | 1 | no | — |
| 148 | D268 | — | 8 | 1 | no | — |
| 149 | D268 | — | 8 | 1 | no | — |
| 150 | C4×D67 | — | 8 | 1 | no | — |
| 151 | C4×D67 | — | 8 | 1 | no | — |
| 152 | Dic134 | — | 4 | 2 | no | — |
| 153 | Dic134 | — | 4 | 1 | no | — |
| 154 | Dic134 | — | 4 | 1 | no | — |
| 155 | Dic134 | — | 8 | 1 | no | — |
| 156 | C8×C67 | — | 8 | 1 | no | — |
| 157 | C8×C67 | — | 8 | 1 | no | — |
| 158 | C67⋊C8 | — | 4 | 2 | no | — |
| 159 | C22×C67 | — | 2 | 1 | no | — |
| 160 | C22×C67 | — | 2 | 1 | no | — |
| 161 | C22×C67 | #449 | 1 | 1 | yes | characteristic |
| 162 | C22×C67 | #453 | 1 | 1 | yes | characteristic |
| 163 | C22×C67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 164 | C2×D67 | — | 8 | 1 | no | — |
| 165 | C2×D67 | — | 8 | 1 | no | — |
| 166 | C2×D67 | — | 8 | 1 | no | — |
| 167 | C4×C67 | — | 2 | 1 | no | — |
| 168 | C4×C67 | — | 2 | 1 | no | — |
| 169 | C4×C67 | — | 4 | 2 | no | — |
| 170 | C4×C67 | — | 4 | 1 | no | — |
| 171 | C4×C67 | — | 4 | 1 | no | — |
| 172 | C4×C67 | — | 8 | 1 | no | — |
| 173 | Dic67 | — | 4 | 2 | no | — |
| 174 | Dic67 | — | 4 | 2 | no | — |
| 175 | Dic67 | — | 4 | 2 | no | — |
| 176 | Dic67 | — | 8 | 1 | no | — |
| 177 | Dic67 | — | 8 | 1 | no | — |
| 178 | #12197 | — | 67 | 1 | no | maximal, Sylow |
| 179 | C2×C67 | — | 2 | 1 | no | — |
| 180 | C2×C67 | — | 2 | 1 | no | — |
| 181 | C2×C67 | #1600 | 1 | 1 | yes | characteristic |
| 182 | C2×C67 | #2197 | 1 | 1 | yes | characteristic |
| 183 | C2×C67 | #2205 | 1 | 1 | yes | characteristic |
| 184 | D67 | — | 16 | 1 | no | — |
| 185 | #2586 | — | 67 | 1 | no | — |
| 186 | #2007 | — | 67 | 1 | no | — |
| 187 | #1610 | — | 67 | 1 | no | — |
| 188 | #1604 | — | 67 | 1 | no | — |
| 189 | #1354 | — | 67 | 1 | no | — |
| 190 | #1346 | — | 67 | 1 | no | — |
| 191 | #1319 | D67 | 1 | 1 | yes | characteristic, complemented |
| 192 | C67 | #12197 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 193 | C2×#137 | — | 134 | 1 | no | — |
| 194 | #537 | — | 67 | 1 | no | — |
| 195 | #480 | — | 134 | 1 | no | — |
| 196 | #448 | — | 134 | 1 | no | — |
| 197 | C2×#104 | — | 134 | 1 | no | — |
| 198 | #398 | — | 67 | 1 | no | — |
| 199 | #395 | — | 67 | 1 | no | — |
| 200 | #395 | — | 134 | 1 | no | — |
| 201 | #391 | — | 134 | 1 | no | — |
| 202 | #391 | C2×D67 | 1 | 1 | yes | characteristic |
| 203 | #389 | — | 134 | 1 | no | — |
| 204 | #387 | — | 134 | 1 | no | — |
| 205 | #387 | — | 134 | 1 | no | — |
| 206 | C4×C4⋊C4 | — | 134 | 1 | no | — |
| 207 | #343 | — | 67 | 1 | no | — |
| 208 | #327 | — | 134 | 1 | no | — |
| 209 | #327 | — | 134 | 1 | no | — |
| 210 | #324 | C2×D67 | 1 | 1 | yes | characteristic |
| 211 | #324 | C2×D67 | 1 | 1 | yes | characteristic |
| 212 | C2×#41 | — | 134 | 1 | no | — |
| 213 | C22×Q8 | — | 67 | 1 | no | — |
| 214 | C22×Q8 | D268 | 1 | 1 | yes | characteristic |
| 215 | #137 | — | 268 | 2 | no | — |
| 216 | #137 | — | 268 | 2 | no | — |
| 217 | C2×Q16 | — | 268 | 1 | no | — |
| 218 | C2×SD16 | — | 268 | 1 | no | — |
| 219 | C2×SD16 | — | 268 | 1 | no | — |
| 220 | C2×M16 | — | 134 | 1 | no | — |
| 221 | C22⋊Q8 | — | 268 | 1 | no | — |
| 222 | #121 | — | 268 | 1 | no | — |
| 223 | #121 | — | 134 | 1 | no | — |
| 224 | #121 | — | 134 | 1 | no | — |
| 225 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 226 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 227 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 228 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 229 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 230 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 231 | C2×C4⋊C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 232 | C2×C42 | — | 134 | 1 | no | — |
| 233 | C2×C42 | — | 134 | 1 | no | — |
| 234 | C2×C42 | D268 | 1 | 1 | yes | characteristic |
| 235 | #107 | — | 268 | 1 | no | — |
| 236 | #104 | — | 268 | 2 | no | — |
| 237 | #103 | — | 268 | 1 | no | — |
| 238 | #102 | — | 268 | 1 | no | — |
| 239 | C22⋊C8 | — | 2 | 1 | no | — |
| 240 | C22⋊C8 | — | 2 | 1 | no | — |
| 241 | #95 | — | 2 | 1 | no | — |
| 242 | #95 | — | 2 | 1 | no | — |
| 243 | #95 | — | 67 | 1 | no | — |
| 244 | #95 | — | 67 | 1 | no | — |
| 245 | #95 | — | 134 | 1 | no | — |
| 246 | #95 | — | 134 | 1 | no | — |
| 247 | #95 | — | 134 | 1 | no | — |
| 248 | #95 | — | 134 | 1 | no | — |
| 249 | #95 | — | 134 | 1 | no | — |
| 250 | #41 | — | 268 | 1 | no | — |
| 251 | #41 | — | 268 | 1 | no | — |
| 252 | #41 | — | 268 | 1 | no | — |
| 253 | #41 | — | 268 | 1 | no | — |
| 254 | C2×Q8 | — | 2 | 1 | no | — |
| 255 | C2×Q8 | — | 2 | 1 | no | — |
| 256 | C2×Q8 | — | 4 | 1 | no | — |
| 257 | C2×Q8 | — | 4 | 1 | no | — |
| 258 | C2×Q8 | — | 268 | 1 | no | — |
| 259 | C2×Q8 | — | 268 | 2 | no | — |
| 260 | C2×Q8 | — | 134 | 1 | no | — |
| 261 | C2×D4 | — | 268 | 1 | no | — |
| 262 | C2×D4 | — | 134 | 1 | no | — |
| 263 | C2×D4 | — | 134 | 1 | no | — |
| 264 | C2×D4 | — | 134 | 1 | no | — |
| 265 | C22×C4 | — | 2 | 1 | no | — |
| 266 | C22×C4 | — | 2 | 1 | no | — |
| 267 | C22×C4 | — | 268 | 1 | no | — |
| 268 | C22×C4 | — | 134 | 1 | no | — |
| 269 | C22×C4 | — | 134 | 1 | no | — |
| 270 | C22×C4 | — | 134 | 1 | no | — |
| 271 | C22×C4 | — | 134 | 1 | no | — |
| 272 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 273 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 274 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 275 | Q16 | — | 268 | 4 | no | — |
| 276 | SD16 | — | 268 | 4 | no | — |
| 277 | SD16 | — | 536 | 2 | no | — |
| 278 | M16 | — | 268 | 1 | no | — |
| 279 | M16 | — | 134 | 2 | no | — |
| 280 | C2×C8 | — | 4 | 1 | no | — |
| 281 | C2×C8 | — | 4 | 1 | no | — |
| 282 | C2×C8 | — | 268 | 1 | no | — |
| 283 | C4⋊C4 | — | 4 | 1 | no | — |
| 284 | C4⋊C4 | — | 268 | 1 | no | — |
| 285 | C4⋊C4 | — | 268 | 2 | no | — |
| 286 | C4⋊C4 | — | 268 | 1 | no | — |
| 287 | C4⋊C4 | — | 268 | 1 | no | — |
| 288 | C4⋊C4 | — | 536 | 1 | no | — |
| 289 | C4⋊C4 | — | 536 | 1 | no | — |
| 290 | C4⋊C4 | — | 134 | 1 | no | — |
| 291 | C4⋊C4 | — | 134 | 1 | no | — |
| 292 | C4⋊C4 | — | 134 | 4 | no | — |
| 293 | C22⋊C4 | — | 268 | 1 | no | — |
| 294 | C22⋊C4 | — | 268 | 1 | no | — |
| 295 | C42 | — | 4 | 1 | no | — |
| 296 | C42 | — | 268 | 2 | no | — |
| 297 | C42 | — | 536 | 1 | no | — |
| 298 | C23 | — | 268 | 1 | no | — |
| 299 | C23 | #14524013 | 1 | 1 | yes | characteristic |
| 300 | Q8 | — | 4 | 2 | no | — |
| 301 | Q8 | — | 8 | 1 | no | — |
| 302 | Q8 | — | 268 | 1 | no | — |
| 303 | Q8 | — | 268 | 1 | no | — |
| 304 | Q8 | — | 268 | 2 | no | — |
| 305 | Q8 | — | 536 | 1 | no | — |
| 306 | D4 | — | 268 | 1 | no | — |
| 307 | D4 | — | 268 | 1 | no | — |
| 308 | D4 | — | 536 | 1 | no | — |
| 309 | D4 | — | 536 | 1 | no | — |
| 310 | D4 | — | 536 | 1 | no | — |
| 311 | D4 | — | 536 | 1 | no | — |
| 312 | C2×C4 | — | 2 | 1 | no | — |
| 313 | C2×C4 | — | 2 | 1 | no | — |
| 314 | C2×C4 | — | 2 | 2 | no | — |
| 315 | C2×C4 | — | 2 | 1 | no | — |
| 316 | C2×C4 | — | 2 | 1 | no | — |
| 317 | C2×C4 | — | 4 | 1 | no | — |
| 318 | C2×C4 | — | 4 | 1 | no | — |
| 319 | C2×C4 | — | 4 | 1 | no | — |
| 320 | C2×C4 | — | 4 | 1 | no | — |
| 321 | C2×C4 | — | 4 | 1 | no | — |
| 322 | C2×C4 | — | 4 | 1 | no | — |
| 323 | C2×C4 | — | 4 | 1 | no | — |
| 324 | C2×C4 | — | 268 | 1 | no | — |
| 325 | C2×C4 | — | 268 | 1 | no | — |
| 326 | C2×C4 | — | 268 | 1 | no | — |
| 327 | C2×C4 | — | 268 | 1 | no | — |
| 328 | C2×C4 | — | 268 | 1 | no | — |
| 329 | C2×C4 | — | 268 | 1 | no | — |
| 330 | C2×C4 | — | 268 | 1 | no | — |
| 331 | C2×C4 | — | 268 | 1 | no | — |
| 332 | C2×C4 | — | 268 | 1 | no | — |
| 333 | C2×C4 | — | 268 | 1 | no | — |
| 334 | C2×C4 | — | 536 | 1 | no | — |
| 335 | C2×C4 | — | 536 | 1 | no | — |
| 336 | C2×C4 | — | 134 | 2 | no | — |
| 337 | C2×C4 | — | 134 | 2 | no | — |
| 338 | C2×C4 | — | 134 | 2 | no | — |
| 339 | C2×C4 | #14524065 | 1 | 1 | yes | characteristic |
| 340 | C2×C4 | #14524071 | 1 | 1 | yes | characteristic |
| 341 | C8 | — | 8 | 1 | no | — |
| 342 | C8 | — | 8 | 1 | no | — |
| 343 | C8 | — | 268 | 2 | no | — |
| 344 | C22 | — | 2 | 1 | no | — |
| 345 | C22 | — | 2 | 1 | no | — |
| 346 | C22 | — | 536 | 1 | no | — |
| 347 | C22 | — | 536 | 1 | no | — |
| 348 | C22 | — | 536 | 1 | no | — |
| 349 | C22 | #16863543 | 1 | 1 | yes | characteristic |
| 350 | C22 | #16863566 | 1 | 1 | yes | characteristic |
| 351 | C22 | #16863584 | 1 | 1 | yes | characteristic |
| 352 | C4 | — | 2 | 1 | no | — |
| 353 | C4 | — | 2 | 1 | no | — |
| 354 | C4 | — | 4 | 2 | no | — |
| 355 | C4 | — | 4 | 1 | no | — |
| 356 | C4 | — | 4 | 1 | no | — |
| 357 | C4 | — | 8 | 1 | no | — |
| 358 | C4 | — | 268 | 2 | no | — |
| 359 | C4 | — | 268 | 2 | no | — |
| 360 | C4 | — | 268 | 2 | no | — |
| 361 | C4 | — | 536 | 1 | no | — |
| 362 | C4 | — | 536 | 1 | no | — |
| 363 | C2 | — | 2 | 1 | no | — |
| 364 | C2 | — | 2 | 1 | no | — |
| 365 | C2 | — | 1072 | 1 | no | — |
| 366 | C2 | #22559157 | 1 | 1 | yes | characteristic |
| 367 | C2 | #22562202 | 1 | 1 | yes | characteristic |
| 368 | C2 | #22562240 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22565620 | C2 | semidirect |
| 5. #22558240 | C2 | semidirect |
| 6. #22558216 | C2 | semidirect |
| 7. C67×#1319 | C2 | semidirect |
| 191. #1319 | D67 | semidirect |
| 192. C67 | #12197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22565620 | 2 |
| #22561255 | 2 |
| #22559214 | 2 |
| #22559180 | 2 |
| #22558240 | 2 |
| #22558216 | 2 |
| C67×#1319 | 2 |
| #12197 | 67 |