Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
3118 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 3118 conjugacy classes of subgroups — too many to draw. Only its 220 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 | #63091 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33531 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #33522 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #32948 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #12745 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #12741 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #12684 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | H(7,𝔽2) | — | 2 | 1 | no | — |
| 9 | #3585 | — | 2 | 12 | no | — |
| 10 | #3585 | — | 2 | 3 | no | — |
| 11 | #3584 | — | 2 | 6 | no | — |
| 12 | #3584 | C22 | 1 | 3 | yes | — |
| 13 | C2×#576 | — | 2 | 6 | no | — |
| 14 | C2×#576 | C22 | 1 | 3 | yes | — |
| 15 | #3573 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#509 | C22 | 1 | 3 | yes | complemented |
| 17 | C22×D16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #3058 | C22 | 1 | 3 | yes | complemented |
| 19 | #3027 | — | 2 | 1 | no | — |
| 20 | #2190 | — | 2 | 12 | no | — |
| 21 | #2186 | — | 2 | 6 | no | — |
| 22 | #2184 | — | 2 | 6 | no | — |
| 23 | #2145 | C22 | 1 | 6 | yes | complemented |
| 24 | #2140 | C22 | 1 | 3 | yes | complemented |
| 25 | #2138 | C22 | 1 | 3 | yes | complemented |
| 26 | #2115 | C22 | 1 | 3 | yes | complemented |
| 27 | #2113 | C22 | 1 | 3 | yes | complemented |
| 28 | #1910 | — | 2 | 3 | no | — |
| 29 | #1812 | C22 | 1 | 3 | yes | complemented |
| 30 | #585 | — | 2 | 12 | no | — |
| 31 | #585 | — | 2 | 3 | no | — |
| 32 | #585 | — | 4 | 6 | no | — |
| 33 | #585 | D4 | 1 | 1 | yes | characteristic |
| 34 | C2×H(5,𝔽2) | — | 2 | 12 | no | — |
| 35 | C2×H(5,𝔽2) | — | 2 | 3 | no | — |
| 36 | C2×H(5,𝔽2) | — | 4 | 6 | no | — |
| 37 | C2×H(5,𝔽2) | — | 4 | 4 | no | — |
| 38 | #578 | — | 2 | 4 | no | — |
| 39 | #578 | — | 2 | 6 | no | — |
| 40 | #577 | — | 2 | 24 | no | — |
| 41 | #577 | — | 2 | 24 | no | — |
| 42 | #577 | — | 2 | 12 | no | — |
| 43 | #576 | — | 2 | 12 | no | — |
| 44 | #576 | — | 2 | 24 | no | — |
| 45 | #576 | — | 2 | 24 | no | — |
| 46 | #576 | — | 2 | 12 | no | — |
| 47 | #576 | — | 2 | 12 | no | — |
| 48 | #576 | — | 2 | 6 | no | — |
| 49 | #575 | — | 2 | 24 | no | — |
| 50 | #575 | — | 2 | 12 | no | — |
| 51 | #575 | — | 2 | 3 | no | — |
| 52 | #575 | D4 | 1 | 12 | yes | complemented |
| 53 | C2×AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 54 | C2×AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 55 | C2×AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 56 | C2×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 57 | C2×#135 | — | 2 | 12 | no | — |
| 58 | C2×#135 | — | 2 | 6 | no | — |
| 59 | C2×#135 | D4 | 1 | 6 | yes | complemented |
| 60 | C2×#135 | C23 | 1 | 3 | yes | — |
| 61 | C22×D8 | — | 2 | 4 | no | — |
| 62 | C22×D8 | D4 | 1 | 6 | yes | complemented |
| 63 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 64 | C22×D8 | C23 | 1 | 1 | yes | characteristic, complemented |
| 65 | #568 | — | 2 | 6 | no | — |
| 66 | #568 | D4 | 1 | 3 | yes | — |
| 67 | C2×#131 | — | 2 | 6 | no | — |
| 68 | C2×#131 | C23 | 1 | 3 | yes | — |
| 69 | #535 | — | 2 | 3 | no | — |
| 70 | #509 | — | 2 | 12 | no | — |
| 71 | C2×SD32 | — | 2 | 3 | no | — |
| 72 | C2×D16 | — | 2 | 6 | no | — |
| 73 | C2×D16 | — | 2 | 3 | no | — |
| 74 | C2×M32 | C23 | 1 | 3 | yes | complemented |
| 75 | C22×C16 | C23 | 1 | 1 | yes | characteristic, complemented |
| 76 | #469 | — | 2 | 6 | no | — |
| 77 | #466 | — | 2 | 6 | no | — |
| 78 | B(4,𝔽2) | — | 4 | 4 | no | — |
| 79 | #427 | C23 | 1 | 3 | yes | complemented |
| 80 | #418 | — | 2 | 3 | no | — |
| 81 | #410 | — | 2 | 3 | no | — |
| 82 | #360 | — | 2 | 12 | no | — |
| 83 | #358 | — | 2 | 3 | no | — |
| 84 | #357 | — | 2 | 3 | no | — |
| 85 | #357 | — | 2 | 6 | no | — |
| 86 | #349 | — | 2 | 6 | no | — |
| 87 | C22⋊C16 | — | 2 | 6 | no | — |
| 88 | H(3,ℤ/4) | — | 2 | 3 | no | — |
| 89 | 2−1+4 | — | 2 | 3 | no | — |
| 90 | 2−1+4 | — | 2 | 8 | no | — |
| 91 | 2−1+4 | — | 2 | 12 | no | — |
| 92 | 2−1+4 | — | 4 | 12 | no | — |
| 93 | 2−1+4 | — | 4 | 3 | no | — |
| 94 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 95 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 96 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 97 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 98 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 99 | H(5,𝔽2) | — | 4 | 24 | no | — |
| 100 | H(5,𝔽2) | — | 4 | 24 | no | — |
| 101 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 102 | H(5,𝔽2) | — | 4 | 24 | no | — |
| 103 | H(5,𝔽2) | — | 4 | 6 | no | — |
| 104 | H(5,𝔽2) | — | 4 | 3 | no | — |
| 105 | H(5,𝔽2) | D8 | 1 | 4 | yes | — |
| 106 | C2×#41 | — | 2 | 6 | no | — |
| 107 | C2×#41 | — | 2 | 24 | no | — |
| 108 | C2×#41 | — | 2 | 12 | no | — |
| 109 | C2×#41 | — | 2 | 6 | no | — |
| 110 | C2×#41 | — | 2 | 3 | no | — |
| 111 | C2×#41 | — | 4 | 12 | no | — |
| 112 | C2×#41 | — | 4 | 24 | no | — |
| 113 | C2×#41 | — | 4 | 12 | no | — |
| 114 | C2×#41 | — | 4 | 24 | no | — |
| 115 | C2×#41 | — | 4 | 3 | no | — |
| 116 | C2×#41 | C2×D4 | 1 | 3 | yes | — |
| 117 | C22×D4 | — | 2 | 8 | no | — |
| 118 | C22×D4 | — | 2 | 6 | no | — |
| 119 | C22×D4 | — | 2 | 1 | no | — |
| 120 | C22×D4 | — | 2 | 1 | no | — |
| 121 | C22×D4 | — | 4 | 12 | no | — |
| 122 | C22×D4 | — | 4 | 24 | no | — |
| 123 | C22×D4 | — | 4 | 6 | no | — |
| 124 | C22×D4 | — | 4 | 3 | no | — |
| 125 | #137 | — | 2 | 24 | no | — |
| 126 | #137 | — | 2 | 12 | no | — |
| 127 | #137 | — | 2 | 24 | no | — |
| 128 | AGL(1,ℤ/8) | — | 2 | 48 | no | — |
| 129 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 130 | AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 131 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 132 | AGL(1,ℤ/8) | — | 2 | 48 | no | — |
| 133 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 134 | #135 | — | 2 | 12 | no | — |
| 135 | #135 | — | 2 | 48 | no | — |
| 136 | #135 | — | 2 | 12 | no | — |
| 137 | #135 | — | 2 | 12 | no | — |
| 138 | #135 | — | 2 | 12 | no | — |
| 139 | #135 | — | 2 | 12 | no | — |
| 140 | #135 | — | 2 | 6 | no | — |
| 141 | #135 | C2×D4 | 1 | 12 | yes | — |
| 142 | C2×Q16 | — | 2 | 6 | no | — |
| 143 | C2×Q16 | C2×D4 | 1 | 3 | yes | — |
| 144 | C2×SD16 | — | 2 | 24 | no | — |
| 145 | C2×SD16 | — | 2 | 12 | no | — |
| 146 | C2×SD16 | — | 2 | 6 | no | — |
| 147 | C2×SD16 | — | 2 | 3 | no | — |
| 148 | C2×D8 | — | 2 | 6 | no | — |
| 149 | C2×D8 | — | 2 | 24 | no | — |
| 150 | C2×D8 | — | 2 | 12 | no | — |
| 151 | C2×D8 | — | 2 | 12 | no | — |
| 152 | C2×D8 | — | 2 | 6 | no | — |
| 153 | C2×D8 | — | 2 | 3 | no | — |
| 154 | C2×D8 | — | 2 | 3 | no | — |
| 155 | C2×D8 | — | 2 | 3 | no | — |
| 156 | C2×D8 | C2×D4 | 1 | 3 | yes | — |
| 157 | C2×D8 | C2×D4 | 1 | 6 | yes | — |
| 158 | #131 | — | 2 | 4 | no | — |
| 159 | #131 | — | 2 | 12 | no | — |
| 160 | #131 | — | 2 | 12 | no | — |
| 161 | #131 | — | 2 | 6 | no | — |
| 162 | #131 | — | 2 | 6 | no | — |
| 163 | C2×M16 | — | 2 | 12 | no | — |
| 164 | C2×M16 | — | 2 | 6 | no | — |
| 165 | C2×M16 | C2×D4 | 1 | 3 | yes | — |
| 166 | C2×M16 | C2×D4 | 1 | 6 | yes | — |
| 167 | C22×C8 | — | 2 | 4 | no | — |
| 168 | C22×C8 | C2×D4 | 1 | 6 | yes | — |
| 169 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 170 | #127 | — | 4 | 3 | no | — |
| 171 | #124 | — | 4 | 3 | no | — |
| 172 | #121 | — | 4 | 6 | no | — |
| 173 | #120 | — | 4 | 6 | no | — |
| 174 | #117 | — | 2 | 3 | no | — |
| 175 | SD32 | — | 4 | 6 | no | — |
| 176 | D16 | — | 4 | 4 | no | — |
| 177 | D16 | — | 4 | 6 | no | — |
| 178 | M32 | — | 2 | 6 | no | — |
| 179 | C2×C16 | — | 2 | 3 | no | — |
| 180 | C2×C16 | — | 2 | 3 | no | — |
| 181 | #107 | — | 2 | 3 | no | — |
| 182 | #106 | — | 2 | 3 | no | — |
| 183 | #102 | — | 4 | 6 | no | — |
| 184 | #99 | — | 4 | 6 | no | — |
| 185 | C24 | — | 4 | 8 | no | — |
| 186 | C24 | — | 4 | 1 | no | — |
| 187 | C24 | — | 4 | 6 | no | — |
| 188 | C24 | — | 4 | 1 | no | — |
| 189 | #41 | — | 2 | 4 | no | — |
| 190 | #41 | — | 2 | 12 | no | — |
| 191 | #41 | — | 2 | 6 | no | — |
| 192 | #41 | — | 2 | 6 | no | — |
| 193 | #41 | — | 2 | 12 | no | — |
| 194 | #41 | — | 2 | 24 | no | — |
| 195 | #41 | — | 2 | 24 | no | — |
| 196 | #41 | — | 2 | 12 | no | — |
| 197 | #41 | — | 4 | 48 | no | — |
| 198 | #41 | — | 4 | 12 | no | — |
| 199 | #41 | — | 4 | 12 | no | — |
| 200 | #41 | — | 4 | 24 | no | — |
| 201 | #41 | — | 4 | 24 | no | — |
| 202 | #41 | — | 4 | 12 | no | — |
| 203 | #41 | — | 4 | 24 | no | — |
| 204 | #41 | — | 4 | 12 | no | — |
| 205 | #41 | — | 4 | 24 | no | — |
| 206 | #41 | — | 4 | 6 | no | — |
| 207 | #41 | — | 4 | 12 | no | — |
| 208 | C2×Q8 | — | 2 | 6 | no | — |
| 209 | C2×Q8 | — | 2 | 12 | no | — |
| 210 | C2×Q8 | — | 2 | 3 | no | — |
| 211 | C2×Q8 | — | 4 | 8 | no | — |
| 212 | C2×Q8 | — | 4 | 12 | no | — |
| 213 | C2×Q8 | AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 214 | C2×D4 | — | 2 | 6 | no | — |
| 215 | C2×D4 | — | 2 | 12 | no | — |
| 216 | C2×D4 | — | 2 | 12 | no | — |
| 217 | C2×D4 | — | 2 | 24 | no | — |
| 218 | C2×D4 | — | 2 | 3 | no | — |
| 219 | C2×D4 | — | 2 | 6 | no | — |
| 220 | C2×D4 | — | 4 | 24 | no | — |
| 221 | C2×D4 | — | 4 | 12 | no | — |
| 222 | C2×D4 | — | 4 | 48 | no | — |
| 223 | C2×D4 | — | 4 | 24 | no | — |
| 224 | C2×D4 | — | 4 | 24 | no | — |
| 225 | C2×D4 | — | 4 | 48 | no | — |
| 226 | C2×D4 | — | 4 | 12 | no | — |
| 227 | C2×D4 | — | 4 | 24 | no | — |
| 228 | C2×D4 | — | 4 | 24 | no | — |
| 229 | C2×D4 | — | 4 | 3 | no | — |
| 230 | C2×D4 | — | 4 | 12 | no | — |
| 231 | C2×D4 | — | 4 | 6 | no | — |
| 232 | C2×D4 | — | 4 | 3 | no | — |
| 233 | C2×D4 | — | 4 | 3 | no | — |
| 234 | C2×D4 | — | 4 | 3 | no | — |
| 235 | C2×D4 | — | 4 | 6 | no | — |
| 236 | C2×D4 | — | 8 | 6 | no | — |
| 237 | C2×D4 | C2×D8 | 1 | 6 | yes | — |
| 238 | C2×D4 | AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 239 | C22×C4 | — | 2 | 4 | no | — |
| 240 | C22×C4 | — | 4 | 24 | no | — |
| 241 | C22×C4 | — | 4 | 12 | no | — |
| 242 | C22×C4 | — | 4 | 3 | no | — |
| 243 | C22×C4 | — | 4 | 6 | no | — |
| 244 | C22×C4 | #120 | 1 | 6 | yes | — |
| 245 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 246 | Q16 | — | 2 | 12 | no | — |
| 247 | Q16 | — | 2 | 3 | no | — |
| 248 | Q16 | #120 | 1 | 6 | yes | — |
| 249 | SD16 | — | 2 | 24 | no | — |
| 250 | SD16 | — | 2 | 24 | no | — |
| 251 | SD16 | — | 2 | 12 | no | — |
| 252 | D8 | — | 2 | 12 | no | — |
| 253 | D8 | — | 2 | 24 | no | — |
| 254 | D8 | — | 2 | 3 | no | — |
| 255 | D8 | — | 2 | 6 | no | — |
| 256 | D8 | — | 4 | 1 | no | — |
| 257 | D8 | — | 4 | 3 | no | — |
| 258 | D8 | #120 | 1 | 4 | yes | — |
| 259 | D8 | #120 | 1 | 6 | yes | — |
| 260 | M16 | — | 2 | 12 | no | — |
| 261 | M16 | — | 2 | 6 | no | — |
| 262 | M16 | — | 2 | 12 | no | — |
| 263 | C2×C8 | — | 2 | 12 | no | — |
| 264 | C2×C8 | — | 2 | 6 | no | — |
| 265 | C2×C8 | — | 2 | 6 | no | — |
| 266 | C2×C8 | #120 | 1 | 6 | yes | — |
| 267 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 268 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 269 | C4⋊C4 | — | 4 | 3 | no | — |
| 270 | C22⋊C4 | — | 4 | 3 | no | — |
| 271 | C22⋊C4 | — | 8 | 6 | no | — |
| 272 | C42 | — | 4 | 3 | no | — |
| 273 | C16 | — | 4 | 1 | no | — |
| 274 | C16 | — | 4 | 3 | no | — |
| 275 | C23 | — | 2 | 4 | no | — |
| 276 | C23 | — | 4 | 24 | no | — |
| 277 | C23 | — | 4 | 12 | no | — |
| 278 | C23 | — | 4 | 3 | no | — |
| 279 | C23 | — | 4 | 6 | no | — |
| 280 | C23 | — | 8 | 3 | no | — |
| 281 | C23 | — | 32 | 1 | no | — |
| 282 | C23 | — | 32 | 1 | no | — |
| 283 | C23 | — | 32 | 6 | no | — |
| 284 | C23 | — | 32 | 8 | no | — |
| 285 | C23 | #447 | 1 | 6 | yes | — |
| 286 | C23 | C22×D8 | 1 | 1 | yes | characteristic |
| 287 | Q8 | — | 2 | 4 | no | — |
| 288 | Q8 | — | 2 | 6 | no | — |
| 289 | Q8 | — | 2 | 6 | no | — |
| 290 | Q8 | — | 4 | 12 | no | — |
| 291 | Q8 | — | 4 | 3 | no | — |
| 292 | D4 | — | 2 | 12 | no | — |
| 293 | D4 | — | 2 | 12 | no | — |
| 294 | D4 | — | 2 | 6 | no | — |
| 295 | D4 | — | 2 | 4 | no | — |
| 296 | D4 | — | 2 | 6 | no | — |
| 297 | D4 | — | 4 | 12 | no | — |
| 298 | D4 | — | 4 | 24 | no | — |
| 299 | D4 | — | 4 | 24 | no | — |
| 300 | D4 | — | 4 | 24 | no | — |
| 301 | D4 | — | 4 | 12 | no | — |
| 302 | D4 | — | 4 | 3 | no | — |
| 303 | D4 | — | 4 | 6 | no | — |
| 304 | D4 | — | 8 | 1 | no | — |
| 305 | D4 | — | 8 | 3 | no | — |
| 306 | D4 | — | 32 | 6 | no | — |
| 307 | C2×C4 | — | 2 | 12 | no | — |
| 308 | C2×C4 | — | 2 | 6 | no | — |
| 309 | C2×C4 | — | 2 | 6 | no | — |
| 310 | C2×C4 | — | 4 | 24 | no | — |
| 311 | C2×C4 | — | 4 | 24 | no | — |
| 312 | C2×C4 | — | 4 | 12 | no | — |
| 313 | C2×C4 | — | 4 | 3 | no | — |
| 314 | C2×C4 | — | 4 | 12 | no | — |
| 315 | C2×C4 | — | 8 | 3 | no | — |
| 316 | C2×C4 | #447 | 1 | 6 | yes | — |
| 317 | C2×C4 | C2×#120 | 1 | 3 | yes | — |
| 318 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 319 | C8 | — | 2 | 6 | no | — |
| 320 | C8 | C2×#120 | 1 | 1 | yes | characteristic |
| 321 | C8 | C2×#120 | 1 | 3 | yes | — |
| 322 | C22 | — | 2 | 6 | no | — |
| 323 | C22 | — | 4 | 1 | no | — |
| 324 | C22 | — | 4 | 6 | no | — |
| 325 | C22 | — | 4 | 4 | no | — |
| 326 | C22 | — | 4 | 6 | no | — |
| 327 | C22 | — | 8 | 4 | no | — |
| 328 | C22 | — | 16 | 6 | no | — |
| 329 | C22 | — | 16 | 3 | no | — |
| 330 | C22 | — | 16 | 6 | no | — |
| 331 | C22 | — | 16 | 24 | no | — |
| 332 | C22 | — | 16 | 12 | no | — |
| 333 | C22 | — | 16 | 1 | no | — |
| 334 | C22 | C2×#447 | 1 | 3 | yes | — |
| 335 | C4 | — | 2 | 6 | no | — |
| 336 | C4 | — | 4 | 6 | no | — |
| 337 | C4 | — | 16 | 3 | no | — |
| 338 | C4 | #2846 | 1 | 1 | yes | characteristic |
| 339 | C4 | #3003 | 1 | 3 | yes | — |
| 340 | C2 | — | 2 | 3 | no | — |
| 341 | C2 | — | 4 | 6 | no | — |
| 342 | C2 | — | 8 | 4 | no | — |
| 343 | C2 | — | 8 | 6 | no | — |
| 344 | C2 | — | 32 | 1 | no | — |
| 345 | C2 | #32878 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #32878 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #3573 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63091 | C2 | semidirect |
| 2. #33531 | C2 | semidirect |
| 3. #33522 | C2 | semidirect |
| 4. #32948 | C2 | semidirect |
| 5. #12745 | C2 | semidirect |
| 6. #12741 | C2 | semidirect |
| 7. #12684 | C2 | semidirect |
| 16. C2×#509 | C22 | semidirect |
| 17. C22×D16 | C22 | semidirect |
| 18. #3058 | C22 | semidirect |
| 23. #2145 | C22 | semidirect |
| 24. #2140 | C22 | semidirect |
| 25. #2138 | C22 | semidirect |
| 26. #2115 | C22 | semidirect |
| 27. #2113 | C22 | semidirect |
| 29. #1812 | C22 | semidirect |
| 52. #575 | D4 | semidirect |
| 59. C2×#135 | D4 | semidirect |
| 62. C22×D8 | D4 | semidirect |
| 64. C22×D8 | C23 | semidirect |
| 74. C2×M32 | C23 | semidirect |
| 75. C22×C16 | C23 | semidirect |
| 79. #427 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63091 | 2 |
| #33531 | 2 |
| #33522 | 2 |
| #32948 | 2 |
| #12745 | 2 |
| #12741 | 2 |
| #12684 | 2 |