Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
726 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 59 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 | #22566544 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22559144 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22558211 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22558141 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C67×#2006 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#14524013 | — | 2 | 2 | no | — |
| 7 | C2×#14524011 | — | 2 | 1 | no | — |
| 8 | #16863529 | — | 2 | 2 | no | — |
| 9 | #16863313 | C22 | 1 | 2 | yes | — |
| 10 | #16863312 | — | 2 | 2 | no | — |
| 11 | #16863298 | — | 2 | 1 | no | — |
| 12 | #16863130 | — | 2 | 2 | no | — |
| 13 | #16863122 | C22 | 1 | 2 | yes | complemented |
| 14 | C2×AGL(1,ℤ/8)×C67 | — | 2 | 1 | no | — |
| 15 | #537×C67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×#104×C67 | — | 2 | 1 | no | — |
| 17 | #390×C67 | C22 | 1 | 1 | yes | characteristic |
| 18 | #343×C67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C24×D67 | — | 2 | 1 | no | — |
| 20 | C22×D268 | — | 2 | 1 | no | — |
| 21 | C22×D268 | D4 | 1 | 2 | yes | — |
| 22 | C22×C22⋊D67 | — | 2 | 2 | no | — |
| 23 | C2×#11761613 | — | 4 | 2 | no | — |
| 24 | #14524013 | — | 4 | 8 | no | — |
| 25 | #14524011 | — | 4 | 2 | no | — |
| 26 | #14524011 | — | 4 | 2 | no | — |
| 27 | C2×C4⋊Dic67 | — | 2 | 1 | no | — |
| 28 | C2×C22⋊Dic67 | — | 2 | 1 | no | — |
| 29 | C2×(C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 30 | C2×(C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 31 | C2×(C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 32 | #14523963 | — | 4 | 2 | no | — |
| 33 | C22⋊(C67⋊C8) | — | 2 | 2 | no | — |
| 34 | C67⋊#95 | D4 | 1 | 2 | yes | — |
| 35 | C2×#41×C67 | — | 2 | 1 | no | — |
| 36 | C22×D4×C67 | D4 | 1 | 1 | yes | characteristic |
| 37 | AGL(1,ℤ/8)×C67 | — | 4 | 2 | no | — |
| 38 | AGL(1,ℤ/8)×C67 | — | 4 | 2 | no | — |
| 39 | C2×SD16×C67 | — | 4 | 1 | no | — |
| 40 | C2×D8×C67 | — | 4 | 1 | no | — |
| 41 | C2×M16×C67 | — | 2 | 1 | no | — |
| 42 | C22⋊Q8×C67 | — | 4 | 1 | no | — |
| 43 | #121×C67 | — | 2 | 2 | no | — |
| 44 | #121×C67 | — | 4 | 1 | no | — |
| 45 | C2×C4⋊C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×C22⋊C4×C67 | — | 2 | 2 | no | — |
| 47 | C2×C42×C67 | D4 | 1 | 1 | yes | characteristic |
| 48 | #104×C67 | — | 4 | 2 | no | — |
| 49 | C23×D67 | — | 2 | 2 | no | — |
| 50 | C23×D67 | — | 4 | 4 | no | — |
| 51 | C23×D67 | — | 4 | 2 | no | — |
| 52 | C23×D67 | — | 8 | 2 | no | — |
| 53 | C23×D67 | — | 8 | 1 | no | — |
| 54 | C23×D67 | — | 8 | 1 | no | — |
| 55 | C2×D268 | — | 2 | 4 | no | — |
| 56 | C2×D268 | — | 4 | 2 | no | — |
| 57 | C2×D268 | — | 4 | 4 | no | — |
| 58 | C2×D268 | — | 8 | 1 | no | — |
| 59 | C2×D268 | — | 8 | 1 | no | — |
| 60 | C2×C22⋊D67 | — | 4 | 4 | no | — |
| 61 | C2×C22⋊D67 | — | 4 | 4 | no | — |
| 62 | C2×C22⋊D67 | — | 8 | 2 | no | — |
| 63 | C22×Dic67 | — | 2 | 2 | no | — |
| 64 | #11761613 | — | 8 | 4 | no | — |
| 65 | C2×C67⋊C8 | — | 4 | 2 | no | — |
| 66 | C4⋊Dic67 | — | 8 | 1 | no | — |
| 67 | C22⋊Dic67 | — | 4 | 2 | no | — |
| 68 | (C2×D67)⋊C4 | — | 4 | 4 | no | — |
| 69 | (C2×D67)⋊C4 | — | 4 | 4 | no | — |
| 70 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 71 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 72 | C24×C67 | — | 2 | 1 | no | — |
| 73 | #41×C67 | — | 4 | 1 | no | — |
| 74 | #41×C67 | — | 4 | 1 | no | — |
| 75 | #41×C67 | — | 4 | 1 | no | — |
| 76 | #41×C67 | — | 4 | 1 | no | — |
| 77 | C2×Q8×C67 | — | 2 | 1 | no | — |
| 78 | C2×D4×C67 | — | 2 | 1 | no | — |
| 79 | C2×D4×C67 | — | 2 | 2 | no | — |
| 80 | C2×D4×C67 | — | 2 | 1 | no | — |
| 81 | C2×D4×C67 | — | 4 | 1 | no | — |
| 82 | C2×D4×C67 | — | 4 | 1 | no | — |
| 83 | C2×D4×C67 | — | 4 | 1 | no | — |
| 84 | C2×D4×C67 | D8 | 1 | 2 | yes | complemented |
| 85 | C22×C4×C67 | — | 2 | 1 | no | — |
| 86 | C22×C4×C67 | — | 4 | 1 | no | — |
| 87 | C22×C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 88 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | SD16×C67 | — | 4 | 4 | no | — |
| 90 | D8×C67 | — | 4 | 4 | no | — |
| 91 | M16×C67 | — | 2 | 2 | no | — |
| 92 | M16×C67 | — | 4 | 1 | no | — |
| 93 | C2×C8×C67 | — | 4 | 1 | no | — |
| 94 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 95 | C4⋊C4×C67 | — | 4 | 1 | no | — |
| 96 | C22⋊C4×C67 | — | 4 | 4 | no | — |
| 97 | C22⋊C4×C67 | — | 4 | 2 | no | — |
| 98 | C42×C67 | — | 4 | 1 | no | — |
| 99 | C23×C67 | — | 2 | 2 | no | — |
| 100 | C23×C67 | — | 4 | 2 | no | — |
| 101 | C23×C67 | — | 4 | 2 | no | — |
| 102 | C23×C67 | — | 4 | 1 | no | — |
| 103 | C23×C67 | — | 4 | 1 | no | — |
| 104 | C23×C67 | — | 4 | 1 | no | — |
| 105 | C23×C67 | #120 | 1 | 1 | yes | characteristic |
| 106 | C22×D67 | — | 2 | 4 | no | — |
| 107 | C22×D67 | — | 4 | 2 | no | — |
| 108 | C22×D67 | — | 4 | 2 | no | — |
| 109 | C22×D67 | — | 4 | 2 | no | — |
| 110 | C22×D67 | — | 4 | 2 | no | — |
| 111 | C22×D67 | — | 4 | 2 | no | — |
| 112 | C22×D67 | — | 4 | 2 | no | — |
| 113 | C22×D67 | — | 8 | 4 | no | — |
| 114 | C22×D67 | — | 8 | 8 | no | — |
| 115 | C22×D67 | — | 8 | 8 | no | — |
| 116 | C22×D67 | — | 8 | 4 | no | — |
| 117 | C22×D67 | — | 8 | 4 | no | — |
| 118 | Q8×C67 | — | 4 | 1 | no | — |
| 119 | Q8×C67 | — | 4 | 1 | no | — |
| 120 | D4×C67 | — | 4 | 2 | no | — |
| 121 | D4×C67 | — | 4 | 1 | no | — |
| 122 | D4×C67 | — | 4 | 1 | no | — |
| 123 | D4×C67 | — | 8 | 1 | no | — |
| 124 | D4×C67 | — | 8 | 2 | no | — |
| 125 | D4×C67 | — | 8 | 1 | no | — |
| 126 | D4×C67 | — | 8 | 1 | no | — |
| 127 | C2×C4×C67 | — | 2 | 1 | no | — |
| 128 | C2×C4×C67 | — | 2 | 1 | no | — |
| 129 | C2×C4×C67 | — | 2 | 2 | no | — |
| 130 | C2×C4×C67 | — | 2 | 2 | no | — |
| 131 | C2×C4×C67 | — | 4 | 1 | no | — |
| 132 | C2×C4×C67 | — | 4 | 1 | no | — |
| 133 | C2×C4×C67 | — | 4 | 2 | no | — |
| 134 | C2×C4×C67 | — | 4 | 1 | no | — |
| 135 | C2×C4×C67 | — | 8 | 1 | no | — |
| 136 | C2×C4×C67 | — | 8 | 1 | no | — |
| 137 | C2×C4×C67 | C2×D8 | 1 | 1 | yes | characteristic |
| 138 | C2×C4×C67 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 139 | C22⋊D67 | — | 8 | 8 | no | — |
| 140 | C2×Dic67 | — | 4 | 2 | no | — |
| 141 | C2×Dic67 | — | 4 | 2 | no | — |
| 142 | C2×Dic67 | — | 4 | 2 | no | — |
| 143 | D268 | — | 4 | 4 | no | — |
| 144 | D268 | — | 8 | 4 | no | — |
| 145 | D268 | — | 8 | 2 | no | — |
| 146 | C8×C67 | — | 4 | 2 | no | — |
| 147 | C67⋊C8 | — | 8 | 2 | no | — |
| 148 | C22×C67 | — | 2 | 1 | no | — |
| 149 | C22×C67 | — | 2 | 1 | no | — |
| 150 | C22×C67 | — | 4 | 4 | no | — |
| 151 | C22×C67 | — | 4 | 2 | no | — |
| 152 | C22×C67 | — | 8 | 2 | no | — |
| 153 | C22×C67 | — | 8 | 1 | no | — |
| 154 | C22×C67 | — | 8 | 1 | no | — |
| 155 | C22×C67 | — | 8 | 1 | no | — |
| 156 | C22×C67 | — | 8 | 1 | no | — |
| 157 | C22×C67 | — | 8 | 1 | no | — |
| 158 | C22×C67 | #447 | 1 | 1 | yes | characteristic |
| 159 | C22×C67 | #453 | 1 | 1 | yes | characteristic |
| 160 | C22×C67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 161 | C2×D67 | — | 4 | 4 | no | — |
| 162 | C2×D67 | — | 4 | 4 | no | — |
| 163 | C2×D67 | — | 4 | 4 | no | — |
| 164 | C2×D67 | — | 8 | 2 | no | — |
| 165 | C2×D67 | — | 8 | 2 | no | — |
| 166 | C2×D67 | — | 8 | 16 | no | — |
| 167 | C2×D67 | — | 8 | 2 | no | — |
| 168 | C2×D67 | — | 8 | 2 | no | — |
| 169 | C4×C67 | — | 2 | 1 | no | — |
| 170 | C4×C67 | — | 2 | 1 | no | — |
| 171 | C4×C67 | — | 4 | 2 | no | — |
| 172 | C4×C67 | — | 4 | 2 | no | — |
| 173 | C4×C67 | — | 8 | 1 | no | — |
| 174 | Dic67 | — | 8 | 2 | no | — |
| 175 | #12096 | — | 67 | 1 | no | maximal, Sylow |
| 176 | C2×C67 | — | 2 | 1 | no | — |
| 177 | C2×C67 | — | 2 | 1 | no | — |
| 178 | C2×C67 | — | 8 | 2 | no | — |
| 179 | C2×C67 | — | 16 | 1 | no | — |
| 180 | C2×C67 | #1595 | 1 | 1 | yes | characteristic |
| 181 | C2×C67 | #2196 | 1 | 1 | yes | characteristic |
| 182 | C2×C67 | #2202 | 1 | 1 | yes | characteristic |
| 183 | D67 | — | 8 | 4 | no | — |
| 184 | #2679 | — | 67 | 1 | no | — |
| 185 | #2006 | D67 | 1 | 1 | yes | characteristic, complemented |
| 186 | #1598 | — | 67 | 2 | no | — |
| 187 | #1345 | — | 67 | 2 | no | — |
| 188 | #1318 | — | 67 | 1 | no | — |
| 189 | C67 | #12096 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 190 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 191 | #537 | C2×D67 | 1 | 1 | yes | characteristic, complemented |
| 192 | C2×#120 | — | 134 | 2 | no | — |
| 193 | C2×#120 | — | 134 | 1 | no | — |
| 194 | #447 | — | 134 | 2 | no | — |
| 195 | C2×#104 | — | 2 | 1 | no | — |
| 196 | #394 | — | 67 | 2 | no | — |
| 197 | #394 | — | 134 | 2 | no | — |
| 198 | #390 | — | 134 | 1 | no | — |
| 199 | #390 | C2×D67 | 1 | 1 | yes | characteristic |
| 200 | #343 | C2×D67 | 1 | 1 | yes | characteristic, complemented |
| 201 | #327 | — | 134 | 2 | no | — |
| 202 | #324 | — | 67 | 2 | no | — |
| 203 | C25 | — | 134 | 1 | no | — |
| 204 | C2×#41 | — | 2 | 1 | no | — |
| 205 | C22×D4 | — | 67 | 2 | no | — |
| 206 | C22×D4 | — | 134 | 1 | no | — |
| 207 | C22×D4 | — | 134 | 2 | no | — |
| 208 | C22×D4 | C22⋊D67 | 1 | 1 | yes | characteristic |
| 209 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 210 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 211 | C2×SD16 | — | 4 | 1 | no | — |
| 212 | C2×D8 | — | 4 | 1 | no | — |
| 213 | C2×D8 | — | 268 | 2 | no | — |
| 214 | C2×M16 | — | 2 | 1 | no | — |
| 215 | C22⋊Q8 | — | 4 | 1 | no | — |
| 216 | #121 | — | 2 | 2 | no | — |
| 217 | #121 | — | 4 | 1 | no | — |
| 218 | #120 | — | 268 | 8 | no | — |
| 219 | #120 | — | 268 | 2 | no | — |
| 220 | #120 | — | 268 | 2 | no | — |
| 221 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 222 | C2×C4⋊C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 223 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 224 | C2×C22⋊C4 | — | 134 | 2 | no | — |
| 225 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 226 | C2×C22⋊C4 | — | 134 | 2 | no | — |
| 227 | C2×C22⋊C4 | — | 134 | 2 | no | — |
| 228 | C2×C42 | C22⋊D67 | 1 | 1 | yes | characteristic |
| 229 | #104 | — | 4 | 2 | no | — |
| 230 | #102 | — | 268 | 2 | no | — |
| 231 | C22⋊C8 | — | 134 | 2 | no | — |
| 232 | #95 | — | 67 | 2 | no | — |
| 233 | C24 | — | 2 | 1 | no | — |
| 234 | C24 | — | 268 | 2 | no | — |
| 235 | C24 | — | 268 | 4 | no | — |
| 236 | C24 | — | 536 | 2 | no | — |
| 237 | C24 | — | 536 | 1 | no | — |
| 238 | C24 | — | 536 | 1 | no | — |
| 239 | C24 | — | 134 | 2 | no | — |
| 240 | #41 | — | 4 | 1 | no | — |
| 241 | #41 | — | 4 | 1 | no | — |
| 242 | #41 | — | 4 | 1 | no | — |
| 243 | #41 | — | 4 | 1 | no | — |
| 244 | C2×Q8 | — | 2 | 1 | no | — |
| 245 | C2×D4 | — | 2 | 1 | no | — |
| 246 | C2×D4 | — | 2 | 2 | no | — |
| 247 | C2×D4 | — | 2 | 1 | no | — |
| 248 | C2×D4 | — | 4 | 1 | no | — |
| 249 | C2×D4 | — | 4 | 1 | no | — |
| 250 | C2×D4 | — | 4 | 1 | no | — |
| 251 | C2×D4 | — | 268 | 2 | no | — |
| 252 | C2×D4 | — | 268 | 4 | no | — |
| 253 | C2×D4 | — | 268 | 4 | no | — |
| 254 | C2×D4 | — | 268 | 4 | no | — |
| 255 | C2×D4 | — | 536 | 1 | no | — |
| 256 | C2×D4 | — | 536 | 1 | no | — |
| 257 | C2×D4 | — | 536 | 2 | no | — |
| 258 | C2×D4 | — | 134 | 4 | no | — |
| 259 | C2×D4 | #11761613 | 1 | 2 | yes | complemented |
| 260 | C22×C4 | — | 2 | 1 | no | — |
| 261 | C22×C4 | — | 4 | 1 | no | — |
| 262 | C22×C4 | — | 134 | 2 | no | — |
| 263 | C22×C4 | D4×D67 | 1 | 2 | yes | — |
| 264 | C22×C4 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 265 | SD16 | — | 4 | 4 | no | — |
| 266 | D8 | — | 4 | 4 | no | — |
| 267 | D8 | — | 536 | 4 | no | — |
| 268 | M16 | — | 2 | 2 | no | — |
| 269 | M16 | — | 4 | 1 | no | — |
| 270 | C2×C8 | — | 4 | 1 | no | — |
| 271 | C2×C8 | — | 268 | 2 | no | — |
| 272 | C4⋊C4 | — | 2 | 2 | no | — |
| 273 | C4⋊C4 | — | 4 | 1 | no | — |
| 274 | C4⋊C4 | — | 536 | 1 | no | — |
| 275 | C22⋊C4 | — | 4 | 4 | no | — |
| 276 | C22⋊C4 | — | 4 | 2 | no | — |
| 277 | C22⋊C4 | — | 268 | 4 | no | — |
| 278 | C22⋊C4 | — | 268 | 4 | no | — |
| 279 | C22⋊C4 | — | 268 | 2 | no | — |
| 280 | C22⋊C4 | — | 268 | 2 | no | — |
| 281 | C22⋊C4 | — | 268 | 2 | no | — |
| 282 | C42 | — | 4 | 1 | no | — |
| 283 | C23 | — | 2 | 2 | no | — |
| 284 | C23 | — | 4 | 2 | no | — |
| 285 | C23 | — | 4 | 2 | no | — |
| 286 | C23 | — | 4 | 1 | no | — |
| 287 | C23 | — | 4 | 1 | no | — |
| 288 | C23 | — | 4 | 1 | no | — |
| 289 | C23 | — | 268 | 2 | no | — |
| 290 | C23 | — | 268 | 2 | no | — |
| 291 | C23 | — | 268 | 2 | no | — |
| 292 | C23 | — | 268 | 2 | no | — |
| 293 | C23 | — | 268 | 2 | no | — |
| 294 | C23 | — | 268 | 2 | no | — |
| 295 | C23 | — | 536 | 8 | no | — |
| 296 | C23 | — | 536 | 4 | no | — |
| 297 | C23 | — | 536 | 4 | no | — |
| 298 | C23 | — | 536 | 8 | no | — |
| 299 | C23 | — | 536 | 4 | no | — |
| 300 | C23 | — | 134 | 4 | no | — |
| 301 | C23 | #14524011 | 1 | 1 | yes | characteristic |
| 302 | Q8 | — | 4 | 1 | no | — |
| 303 | Q8 | — | 4 | 1 | no | — |
| 304 | D4 | — | 4 | 2 | no | — |
| 305 | D4 | — | 4 | 1 | no | — |
| 306 | D4 | — | 4 | 1 | no | — |
| 307 | D4 | — | 8 | 1 | no | — |
| 308 | D4 | — | 8 | 2 | no | — |
| 309 | D4 | — | 8 | 1 | no | — |
| 310 | D4 | — | 8 | 1 | no | — |
| 311 | D4 | — | 268 | 4 | no | — |
| 312 | D4 | — | 536 | 2 | no | — |
| 313 | D4 | — | 536 | 4 | no | — |
| 314 | D4 | — | 536 | 8 | no | — |
| 315 | C2×C4 | — | 2 | 1 | no | — |
| 316 | C2×C4 | — | 2 | 1 | no | — |
| 317 | C2×C4 | — | 2 | 2 | no | — |
| 318 | C2×C4 | — | 2 | 2 | no | — |
| 319 | C2×C4 | — | 4 | 1 | no | — |
| 320 | C2×C4 | — | 4 | 1 | no | — |
| 321 | C2×C4 | — | 4 | 2 | no | — |
| 322 | C2×C4 | — | 4 | 1 | no | — |
| 323 | C2×C4 | — | 8 | 1 | no | — |
| 324 | C2×C4 | — | 8 | 1 | no | — |
| 325 | C2×C4 | — | 268 | 2 | no | — |
| 326 | C2×C4 | — | 268 | 2 | no | — |
| 327 | C2×C4 | — | 268 | 2 | no | — |
| 328 | C2×C4 | C2×#11761613 | 1 | 1 | yes | characteristic |
| 329 | C2×C4 | #14524068 | 1 | 1 | yes | characteristic |
| 330 | C8 | — | 4 | 2 | no | — |
| 331 | C8 | — | 536 | 2 | no | — |
| 332 | C22 | — | 2 | 1 | no | — |
| 333 | C22 | — | 2 | 1 | no | — |
| 334 | C22 | — | 4 | 4 | no | — |
| 335 | C22 | — | 4 | 2 | no | — |
| 336 | C22 | — | 8 | 2 | no | — |
| 337 | C22 | — | 8 | 1 | no | — |
| 338 | C22 | — | 8 | 1 | no | — |
| 339 | C22 | — | 8 | 1 | no | — |
| 340 | C22 | — | 8 | 1 | no | — |
| 341 | C22 | — | 8 | 1 | no | — |
| 342 | C22 | — | 268 | 4 | no | — |
| 343 | C22 | — | 268 | 4 | no | — |
| 344 | C22 | — | 268 | 4 | no | — |
| 345 | C22 | — | 536 | 2 | no | — |
| 346 | C22 | — | 536 | 2 | no | — |
| 347 | C22 | — | 536 | 16 | no | — |
| 348 | C22 | — | 536 | 2 | no | — |
| 349 | C22 | — | 536 | 2 | no | — |
| 350 | C22 | #16863529 | 1 | 1 | yes | characteristic |
| 351 | C22 | #16863563 | 1 | 1 | yes | characteristic |
| 352 | C22 | #16863582 | 1 | 1 | yes | characteristic |
| 353 | C4 | — | 2 | 1 | no | — |
| 354 | C4 | — | 2 | 1 | no | — |
| 355 | C4 | — | 4 | 2 | no | — |
| 356 | C4 | — | 4 | 2 | no | — |
| 357 | C4 | — | 8 | 1 | no | — |
| 358 | C4 | — | 536 | 2 | no | — |
| 359 | C2 | — | 2 | 1 | no | — |
| 360 | C2 | — | 2 | 1 | no | — |
| 361 | C2 | — | 8 | 2 | no | — |
| 362 | C2 | — | 16 | 1 | no | — |
| 363 | C2 | — | 536 | 4 | no | — |
| 364 | C2 | #22559126 | 1 | 1 | yes | characteristic |
| 365 | C2 | #22562192 | 1 | 1 | yes | characteristic |
| 366 | C2 | #22562225 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22566544 | C2 | semidirect |
| 2. #22559144 | C2 | semidirect |
| 3. #22558211 | C2 | semidirect |
| 4. #22558141 | C2 | semidirect |
| 5. C67×#2006 | C2 | semidirect |
| 13. #16863122 | C22 | semidirect |
| 15. #537×C67 | C22 | semidirect |
| 18. #343×C67 | C22 | semidirect |
| 84. C2×D4×C67 | D8 | semidirect |
| 185. #2006 | D67 | semidirect |
| 189. C67 | #12096 | semidirect |
| 191. #537 | C2×D67 | semidirect |
| 200. #343 | C2×D67 | semidirect |
| 259. C2×D4 | #11761613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22566544 | 2 |
| #22559144 | 2 |
| #22558211 | 2 |
| #22558141 | 2 |
| C67×#2006 | 2 |
| #12096 | 67 |