Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2930 conjugacy classes of subgroups; only the 570 normal subgroups are shown.
This group has 2930 conjugacy classes of subgroups — too many to draw. Only its 570 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 | C2×#3567 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#3217 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #19096 | C2 | 1 | 16 | yes | maximal, direct product factor |
| 4 | C2×#1658 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#1656 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C2×#1535 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #3567 | — | 2 | 12 | no | — |
| 8 | #3567 | C22 | 1 | 8 | yes | complemented |
| 9 | C2×#564 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×#562 | C22 | 1 | 3 | yes | complemented |
| 11 | C2×#553 | — | 2 | 3 | no | — |
| 12 | C2×#552 | — | 2 | 3 | no | — |
| 13 | C2×#540 | — | 2 | 3 | no | — |
| 14 | C2×#539 | — | 2 | 3 | no | — |
| 15 | C22×#127 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#529 | C22 | 1 | 3 | yes | — |
| 17 | #3217 | — | 2 | 12 | no | — |
| 18 | #3217 | C22 | 1 | 24 | yes | complemented |
| 19 | C2×#496 | C22 | 1 | 6 | yes | — |
| 20 | C2×#490 | C22 | 1 | 6 | yes | — |
| 21 | C2×#460 | — | 2 | 3 | no | — |
| 22 | C2×#459 | — | 2 | 3 | no | — |
| 23 | C2×#450 | — | 2 | 3 | no | — |
| 24 | C2×#447 | — | 2 | 3 | no | — |
| 25 | C2×#432 | C22 | 1 | 3 | yes | — |
| 26 | #1658 | C22 | 1 | 16 | yes | complemented |
| 27 | #1656 | C22 | 1 | 48 | yes | complemented |
| 28 | #1535 | C22 | 1 | 24 | yes | complemented |
| 29 | C2×#330 | C22 | 1 | 6 | yes | complemented |
| 30 | C2×#329 | C22 | 1 | 6 | yes | complemented |
| 31 | C23×D4 | — | 2 | 3 | no | — |
| 32 | C22×SD16 | — | 2 | 6 | no | — |
| 33 | C22×D8 | — | 2 | 6 | no | — |
| 34 | #564 | — | 2 | 6 | no | — |
| 35 | #564 | C23 | 1 | 4 | yes | complemented |
| 36 | #562 | — | 2 | 6 | no | — |
| 37 | #562 | — | 2 | 6 | no | — |
| 38 | #562 | — | 2 | 6 | no | — |
| 39 | #562 | C23 | 1 | 12 | yes | complemented |
| 40 | #553 | — | 2 | 24 | no | — |
| 41 | #553 | — | 2 | 24 | no | — |
| 42 | #552 | — | 2 | 24 | no | — |
| 43 | #552 | — | 2 | 24 | no | — |
| 44 | #540 | — | 2 | 24 | no | — |
| 45 | #540 | — | 2 | 24 | no | — |
| 46 | #539 | — | 2 | 24 | no | — |
| 47 | #539 | — | 2 | 24 | no | — |
| 48 | C2×#127 | — | 2 | 1 | no | — |
| 49 | C2×#127 | — | 2 | 6 | no | — |
| 50 | C2×#127 | — | 2 | 3 | no | — |
| 51 | C2×#127 | C23 | 1 | 2 | yes | — |
| 52 | C2×#127 | C23 | 1 | 4 | yes | — |
| 53 | #529 | — | 2 | 6 | no | — |
| 54 | #529 | — | 2 | 6 | no | — |
| 55 | #529 | D4 | 1 | 12 | yes | — |
| 56 | #529 | C23 | 1 | 12 | yes | — |
| 57 | C2×#126 | — | 2 | 1 | no | — |
| 58 | C2×#126 | — | 2 | 3 | no | — |
| 59 | C2×#126 | — | 2 | 3 | no | — |
| 60 | C2×#125 | — | 2 | 3 | no | — |
| 61 | C2×#125 | — | 2 | 3 | no | — |
| 62 | C2×#125 | — | 2 | 3 | no | — |
| 63 | C2×#125 | C23 | 1 | 3 | yes | — |
| 64 | C2×#124 | C23 | 1 | 3 | yes | — |
| 65 | C2×#123 | — | 2 | 3 | no | — |
| 66 | C2×#123 | — | 2 | 3 | no | — |
| 67 | C2×#123 | — | 2 | 3 | no | — |
| 68 | C2×#123 | — | 2 | 3 | no | — |
| 69 | C2×#123 | — | 2 | 3 | no | — |
| 70 | C2×C22⋊Q8 | — | 2 | 3 | no | — |
| 71 | C2×C22⋊Q8 | — | 2 | 3 | no | — |
| 72 | C2×C22⋊Q8 | D4 | 1 | 3 | yes | — |
| 73 | C2×#121 | — | 2 | 3 | no | — |
| 74 | C2×#121 | — | 2 | 3 | no | — |
| 75 | C2×#121 | — | 2 | 3 | no | — |
| 76 | C2×#121 | — | 2 | 3 | no | — |
| 77 | C2×#121 | D4 | 1 | 3 | yes | — |
| 78 | C2×C4×Q8 | D4 | 1 | 3 | yes | — |
| 79 | C2×C4×D4 | — | 2 | 3 | no | — |
| 80 | C2×C4×D4 | — | 2 | 3 | no | — |
| 81 | C2×C4×D4 | — | 2 | 3 | no | — |
| 82 | C2×C4×D4 | D4 | 1 | 3 | yes | — |
| 83 | C2×#117 | — | 2 | 3 | no | — |
| 84 | C2×#117 | — | 2 | 3 | no | — |
| 85 | C22×C4⋊C4 | — | 2 | 3 | no | — |
| 86 | C22×C42 | C23 | 1 | 1 | yes | characteristic |
| 87 | #496 | — | 2 | 12 | no | — |
| 88 | #496 | C23 | 1 | 24 | yes | — |
| 89 | #490 | — | 2 | 12 | no | — |
| 90 | #490 | C23 | 1 | 24 | yes | — |
| 91 | #460 | — | 2 | 24 | no | — |
| 92 | #459 | — | 2 | 24 | no | — |
| 93 | #450 | — | 2 | 24 | no | — |
| 94 | #447 | — | 2 | 24 | no | — |
| 95 | #432 | — | 2 | 6 | no | — |
| 96 | #432 | C23 | 1 | 12 | yes | — |
| 97 | C2×C4⋊C8 | — | 2 | 3 | no | — |
| 98 | C2×#102 | — | 2 | 6 | no | — |
| 99 | C2×#102 | — | 2 | 6 | no | — |
| 100 | C2×C22⋊C8 | — | 2 | 3 | no | — |
| 101 | C2×#97 | C23 | 1 | 6 | yes | — |
| 102 | #330 | C23 | 1 | 24 | yes | complemented |
| 103 | #329 | C23 | 1 | 24 | yes | complemented |
| 104 | C25 | — | 4 | 1 | no | — |
| 105 | C22×Q8 | C2×D4 | 1 | 3 | yes | — |
| 106 | C22×D4 | — | 2 | 3 | no | — |
| 107 | C22×D4 | — | 2 | 3 | no | — |
| 108 | C22×D4 | — | 2 | 3 | no | — |
| 109 | C22×D4 | — | 2 | 6 | no | — |
| 110 | C22×D4 | — | 2 | 12 | no | — |
| 111 | C22×D4 | — | 4 | 3 | no | — |
| 112 | C22×D4 | — | 4 | 6 | no | — |
| 113 | C22×D4 | — | 8 | 12 | no | — |
| 114 | C22×D4 | C2×D4 | 1 | 3 | yes | — |
| 115 | C23×C4 | — | 2 | 3 | no | — |
| 116 | C23×C4 | — | 2 | 3 | no | — |
| 117 | C23×C4 | — | 2 | 3 | no | — |
| 118 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 119 | C2×SD16 | — | 2 | 24 | no | — |
| 120 | C2×SD16 | — | 8 | 12 | no | — |
| 121 | C2×D8 | — | 2 | 24 | no | — |
| 122 | C2×D8 | — | 8 | 12 | no | — |
| 123 | C22×C8 | — | 2 | 6 | no | — |
| 124 | #127 | — | 2 | 8 | no | — |
| 125 | #127 | — | 2 | 12 | no | — |
| 126 | #127 | — | 2 | 6 | no | — |
| 127 | #127 | — | 4 | 6 | no | — |
| 128 | #127 | C24 | 1 | 4 | yes | — |
| 129 | #126 | — | 2 | 8 | no | — |
| 130 | #126 | — | 2 | 24 | no | — |
| 131 | #126 | — | 2 | 12 | no | — |
| 132 | #126 | — | 2 | 12 | no | — |
| 133 | #125 | — | 2 | 24 | no | — |
| 134 | #125 | — | 2 | 12 | no | — |
| 135 | #125 | — | 2 | 12 | no | — |
| 136 | #125 | — | 2 | 12 | no | — |
| 137 | #125 | — | 2 | 12 | no | — |
| 138 | #125 | — | 2 | 3 | no | — |
| 139 | #125 | — | 2 | 3 | no | — |
| 140 | #125 | C2×D4 | 1 | 6 | yes | — |
| 141 | #125 | C24 | 1 | 6 | yes | — |
| 142 | #124 | — | 2 | 3 | no | — |
| 143 | #124 | — | 2 | 3 | no | — |
| 144 | #124 | C2×D4 | 1 | 6 | yes | — |
| 145 | #124 | C24 | 1 | 6 | yes | — |
| 146 | #123 | — | 2 | 24 | no | — |
| 147 | #123 | — | 2 | 12 | no | — |
| 148 | #123 | — | 2 | 24 | no | — |
| 149 | #123 | — | 2 | 12 | no | — |
| 150 | #123 | — | 2 | 12 | no | — |
| 151 | #123 | — | 2 | 12 | no | — |
| 152 | #123 | — | 2 | 12 | no | — |
| 153 | #123 | — | 2 | 12 | no | — |
| 154 | C22⋊Q8 | — | 2 | 12 | no | — |
| 155 | C22⋊Q8 | — | 2 | 12 | no | — |
| 156 | C22⋊Q8 | — | 2 | 12 | no | — |
| 157 | C22⋊Q8 | — | 2 | 12 | no | — |
| 158 | C22⋊Q8 | — | 2 | 6 | no | — |
| 159 | C22⋊Q8 | C2×D4 | 1 | 12 | yes | — |
| 160 | #121 | — | 2 | 24 | no | — |
| 161 | #121 | — | 2 | 24 | no | — |
| 162 | #121 | — | 2 | 12 | no | — |
| 163 | #121 | — | 2 | 12 | no | — |
| 164 | #121 | — | 2 | 12 | no | — |
| 165 | #121 | — | 2 | 12 | no | — |
| 166 | #121 | — | 2 | 6 | no | — |
| 167 | #121 | C2×D4 | 1 | 12 | yes | — |
| 168 | C4×Q8 | — | 2 | 6 | no | — |
| 169 | C4×Q8 | C2×D4 | 1 | 12 | yes | — |
| 170 | C4×D4 | — | 2 | 24 | no | — |
| 171 | C4×D4 | — | 2 | 24 | no | — |
| 172 | C4×D4 | — | 2 | 12 | no | — |
| 173 | C4×D4 | — | 2 | 12 | no | — |
| 174 | C4×D4 | — | 2 | 6 | no | — |
| 175 | C4×D4 | C2×D4 | 1 | 12 | yes | — |
| 176 | #117 | — | 2 | 24 | no | — |
| 177 | #117 | — | 2 | 12 | no | — |
| 178 | #117 | — | 2 | 12 | no | — |
| 179 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 180 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 181 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 182 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 183 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 184 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 185 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 186 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 187 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 188 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 189 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 190 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 191 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 192 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 193 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 194 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 195 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 196 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 197 | C2×C42 | — | 2 | 1 | no | — |
| 198 | C2×C42 | — | 2 | 1 | no | — |
| 199 | C2×C42 | — | 2 | 3 | no | — |
| 200 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 201 | C2×C42 | C2×D4 | 1 | 6 | yes | — |
| 202 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 203 | C2×C42 | C24 | 1 | 2 | yes | — |
| 204 | C4⋊C8 | — | 2 | 12 | no | — |
| 205 | #102 | — | 2 | 24 | no | — |
| 206 | #102 | — | 2 | 24 | no | — |
| 207 | C22⋊C8 | — | 2 | 12 | no | — |
| 208 | #97 | — | 2 | 6 | no | — |
| 209 | #97 | C24 | 1 | 12 | yes | — |
| 210 | C24 | — | 2 | 3 | no | — |
| 211 | C24 | — | 4 | 4 | no | — |
| 212 | C24 | — | 4 | 2 | no | — |
| 213 | C24 | — | 8 | 12 | no | — |
| 214 | C24 | #120 | 1 | 1 | yes | characteristic |
| 215 | C2×Q8 | — | 2 | 3 | no | — |
| 216 | C2×Q8 | — | 4 | 6 | no | — |
| 217 | C2×Q8 | C22×D4 | 1 | 6 | yes | — |
| 218 | C2×D4 | — | 2 | 12 | no | — |
| 219 | C2×D4 | — | 2 | 12 | no | — |
| 220 | C2×D4 | — | 2 | 12 | no | — |
| 221 | C2×D4 | — | 2 | 3 | no | — |
| 222 | C2×D4 | — | 2 | 12 | no | — |
| 223 | C2×D4 | — | 4 | 6 | no | — |
| 224 | C2×D4 | — | 4 | 12 | no | — |
| 225 | C2×D4 | — | 4 | 12 | no | — |
| 226 | C2×D4 | — | 4 | 12 | no | — |
| 227 | C2×D4 | — | 4 | 6 | no | — |
| 228 | C2×D4 | — | 8 | 12 | no | — |
| 229 | C2×D4 | — | 8 | 24 | no | — |
| 230 | C2×D4 | — | 8 | 6 | no | — |
| 231 | C2×D4 | — | 8 | 6 | no | — |
| 232 | C2×D4 | — | 8 | 6 | no | — |
| 233 | C2×D4 | — | 8 | 24 | no | — |
| 234 | C2×D4 | C22×D4 | 1 | 6 | yes | — |
| 235 | C22×C4 | — | 2 | 3 | no | — |
| 236 | C22×C4 | — | 2 | 3 | no | — |
| 237 | C22×C4 | — | 2 | 3 | no | — |
| 238 | C22×C4 | — | 2 | 12 | no | — |
| 239 | C22×C4 | — | 2 | 12 | no | — |
| 240 | C22×C4 | — | 2 | 12 | no | — |
| 241 | C22×C4 | — | 4 | 6 | no | — |
| 242 | C22×C4 | — | 8 | 6 | no | — |
| 243 | C22×C4 | — | 8 | 6 | no | — |
| 244 | C22×C4 | — | 8 | 6 | no | — |
| 245 | C22×C4 | #120 | 1 | 3 | yes | — |
| 246 | C22×C4 | #120 | 1 | 6 | yes | — |
| 247 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 248 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 249 | SD16 | — | 8 | 24 | no | — |
| 250 | D8 | — | 8 | 24 | no | — |
| 251 | C2×C8 | — | 2 | 12 | no | — |
| 252 | C2×C8 | — | 4 | 12 | no | — |
| 253 | C4⋊C4 | — | 2 | 12 | no | — |
| 254 | C4⋊C4 | — | 2 | 12 | no | — |
| 255 | C4⋊C4 | — | 2 | 12 | no | — |
| 256 | C4⋊C4 | — | 2 | 12 | no | — |
| 257 | C4⋊C4 | — | 2 | 12 | no | — |
| 258 | C4⋊C4 | — | 2 | 12 | no | — |
| 259 | C4⋊C4 | — | 2 | 6 | no | — |
| 260 | C4⋊C4 | — | 2 | 6 | no | — |
| 261 | C4⋊C4 | — | 2 | 3 | no | — |
| 262 | C4⋊C4 | — | 2 | 3 | no | — |
| 263 | C4⋊C4 | — | 2 | 6 | no | — |
| 264 | C4⋊C4 | — | 2 | 6 | no | — |
| 265 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 266 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 267 | C22⋊C4 | — | 2 | 12 | no | — |
| 268 | C22⋊C4 | — | 2 | 12 | no | — |
| 269 | C22⋊C4 | — | 2 | 12 | no | — |
| 270 | C22⋊C4 | — | 2 | 12 | no | — |
| 271 | C22⋊C4 | — | 2 | 6 | no | — |
| 272 | C22⋊C4 | — | 2 | 12 | no | — |
| 273 | C22⋊C4 | — | 2 | 6 | no | — |
| 274 | C22⋊C4 | — | 2 | 6 | no | — |
| 275 | C22⋊C4 | — | 2 | 6 | no | — |
| 276 | C42 | — | 2 | 4 | no | — |
| 277 | C42 | — | 2 | 4 | no | — |
| 278 | C42 | — | 2 | 12 | no | — |
| 279 | C42 | #120 | 1 | 6 | yes | — |
| 280 | C42 | C22×D4 | 1 | 3 | yes | — |
| 281 | C42 | C22×D4 | 1 | 6 | yes | — |
| 282 | C42 | C25 | 1 | 1 | yes | characteristic |
| 283 | C23 | — | 2 | 6 | no | — |
| 284 | C23 | — | 2 | 6 | no | — |
| 285 | C23 | — | 4 | 6 | no | — |
| 286 | C23 | — | 4 | 6 | no | — |
| 287 | C23 | — | 4 | 6 | no | — |
| 288 | C23 | — | 4 | 4 | no | — |
| 289 | C23 | — | 8 | 24 | no | — |
| 290 | C23 | — | 8 | 12 | no | — |
| 291 | C23 | — | 16 | 16 | no | — |
| 292 | C23 | C2×#120 | 1 | 2 | yes | — |
| 293 | C23 | C2×#120 | 1 | 1 | yes | characteristic |
| 294 | Q8 | — | 4 | 6 | no | — |
| 295 | Q8 | — | 8 | 3 | no | — |
| 296 | D4 | — | 4 | 6 | no | — |
| 297 | D4 | — | 4 | 12 | no | — |
| 298 | D4 | — | 4 | 12 | no | — |
| 299 | D4 | — | 8 | 3 | no | — |
| 300 | D4 | — | 8 | 12 | no | — |
| 301 | D4 | — | 8 | 24 | no | — |
| 302 | D4 | — | 8 | 12 | no | — |
| 303 | D4 | — | 8 | 12 | no | — |
| 304 | D4 | — | 8 | 12 | no | — |
| 305 | C2×C4 | — | 2 | 6 | no | — |
| 306 | C2×C4 | — | 2 | 6 | no | — |
| 307 | C2×C4 | — | 2 | 6 | no | — |
| 308 | C2×C4 | — | 2 | 6 | no | — |
| 309 | C2×C4 | — | 2 | 6 | no | — |
| 310 | C2×C4 | — | 4 | 6 | no | — |
| 311 | C2×C4 | — | 4 | 6 | no | — |
| 312 | C2×C4 | — | 4 | 6 | no | — |
| 313 | C2×C4 | — | 4 | 6 | no | — |
| 314 | C2×C4 | — | 4 | 6 | no | — |
| 315 | C2×C4 | — | 8 | 12 | no | — |
| 316 | C2×C4 | — | 8 | 12 | no | — |
| 317 | C2×C4 | — | 8 | 12 | no | — |
| 318 | C2×C4 | C2×#120 | 1 | 6 | yes | — |
| 319 | C2×C4 | C2×#120 | 1 | 3 | yes | — |
| 320 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 321 | C8 | — | 4 | 12 | no | — |
| 322 | C22 | — | 2 | 6 | no | — |
| 323 | C22 | — | 4 | 4 | no | — |
| 324 | C22 | — | 4 | 6 | no | — |
| 325 | C22 | — | 4 | 6 | no | — |
| 326 | C22 | — | 4 | 6 | no | — |
| 327 | C22 | — | 8 | 12 | no | — |
| 328 | C22 | — | 8 | 12 | no | — |
| 329 | C22 | — | 16 | 16 | no | — |
| 330 | C22 | — | 16 | 8 | no | — |
| 331 | C22 | #3021 | 1 | 6 | yes | — |
| 332 | C22 | C22×#120 | 1 | 1 | yes | characteristic |
| 333 | C4 | — | 2 | 3 | no | — |
| 334 | C4 | — | 2 | 6 | no | — |
| 335 | C4 | — | 2 | 3 | no | — |
| 336 | C4 | — | 4 | 6 | no | — |
| 337 | C4 | — | 4 | 6 | no | — |
| 338 | C4 | — | 4 | 6 | no | — |
| 339 | C2 | — | 4 | 2 | no | — |
| 340 | C2 | — | 8 | 6 | no | — |
| 341 | C2 | — | 16 | 4 | no | — |
| 342 | C2 | #19096 | 1 | 4 | yes | direct product factor |
| 343 | C2 | C2×#3021 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C25 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3567 | C2 | semidirect |
| 2. C2×#3217 | C2 | semidirect |
| 3. #19096 | C2 | direct (N × H) |
| 4. C2×#1658 | C2 | semidirect |
| 5. C2×#1656 | C2 | semidirect |
| 6. C2×#1535 | C2 | semidirect |
| 8. #3567 | C22 | semidirect |
| 9. C2×#564 | C22 | semidirect |
| 10. C2×#562 | C22 | semidirect |
| 18. #3217 | C22 | semidirect |
| 26. #1658 | C22 | semidirect |
| 27. #1656 | C22 | semidirect |
| 28. #1535 | C22 | semidirect |
| 29. C2×#330 | C22 | semidirect |
| 30. C2×#329 | C22 | semidirect |
| 35. #564 | C23 | semidirect |
| 39. #562 | C23 | semidirect |
| 102. #330 | C23 | semidirect |
| 103. #329 | C23 | semidirect |
| 342. C2 | #19096 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3567 | 2 |
| C2×#3217 | 2 |
| #19096 | 2 |
| C2×#1658 | 2 |
| C2×#1656 | 2 |
| C2×#1535 | 2 |