← #34034117
Subgroups — #34034117
Order 18688.
418 conjugacy classes of subgroups.
The subgroup lattice has 356 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22627182 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22627111 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22627094 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22627087 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22627012 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22627005 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22625707 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #17989709 | C4 | 1 | 2 | yes | complemented |
| 9 | #17989708 | — | 2 | 2 | no | — |
| 10 | #17989708 | C4 | 1 | 2 | yes | complemented |
| 11 | #17989706 | — | 2 | 1 | no | — |
| 12 | #17989706 | C22 | 1 | 1 | yes | characteristic |
| 13 | #17989706 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#14556686 | — | 2 | 1 | no | — |
| 15 | C2×#14556686 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#14556686 | C22 | 1 | 1 | yes | characteristic |
| 17 | #17989688 | C4 | 1 | 2 | yes | complemented |
| 18 | #17989687 | C4 | 1 | 2 | yes | complemented |
| 19 | #17989682 | — | 2 | 1 | no | — |
| 20 | #17989681 | — | 2 | 2 | no | — |
| 21 | #64408⋊C16 | — | 2 | 1 | no | — |
| 22 | D73⋊#131 | C22 | 1 | 1 | yes | characteristic |
| 23 | #17989577 | C4 | 1 | 1 | yes | characteristic |
| 24 | #17989553 | C22 | 1 | 1 | yes | characteristic |
| 25 | C4×#11924036 | C22 | 1 | 1 | yes | characteristic |
| 26 | #17989462 | C4 | 1 | 1 | yes | characteristic |
| 27 | #17989458 | C4 | 1 | 1 | yes | characteristic |
| 28 | #104×D73 | C4 | 1 | 1 | yes | characteristic |
| 29 | #14556688 | — | 2 | 2 | no | — |
| 30 | #14556688 | C2×C4 | 1 | 2 | yes | — |
| 31 | #14556688 | C2×C4 | 1 | 2 | yes | — |
| 32 | #14556687 | — | 2 | 2 | no | — |
| 33 | #14556687 | — | 2 | 1 | no | — |
| 34 | #14556687 | — | 2 | 1 | no | — |
| 35 | #14556686 | — | 2 | 2 | no | — |
| 36 | #14556686 | — | 2 | 1 | no | — |
| 37 | #14556686 | — | 2 | 1 | no | — |
| 38 | #14556686 | — | 2 | 1 | no | — |
| 39 | #14556686 | C2×C4 | 1 | 2 | yes | — |
| 40 | #14556686 | C2×C4 | 1 | 2 | yes | — |
| 41 | #14556686 | D4 | 1 | 1 | yes | characteristic |
| 42 | #14556686 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×#11924040 | — | 2 | 2 | no | — |
| 44 | C2×#11924040 | — | 2 | 1 | no | — |
| 45 | C2×#11924040 | D4 | 1 | 2 | yes | — |
| 46 | #14556679 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | #14556679 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | #14556678 | — | 2 | 1 | no | — |
| 49 | #14556678 | — | 2 | 1 | no | — |
| 50 | #14556678 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | #14556678 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | D73⋊M16 | — | 2 | 1 | no | — |
| 53 | D73⋊M16 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C2×#11924036 | — | 2 | 1 | no | — |
| 55 | C2×#11924036 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C2×#11924036 | C23 | 1 | 1 | yes | characteristic |
| 57 | #14556670 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | #14556654 | C8 | 1 | 2 | yes | — |
| 59 | #14556653 | C8 | 1 | 2 | yes | — |
| 60 | #14556645 | — | 2 | 1 | no | — |
| 61 | C4×#10596833 | — | 2 | 1 | no | — |
| 62 | C4×#10596833 | — | 2 | 1 | no | — |
| 63 | C8×#64408 | — | 2 | 1 | no | — |
| 64 | #41×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | M16×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C42×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | #14556519 | C8 | 1 | 1 | yes | characteristic |
| 68 | #14556518 | C8 | 1 | 1 | yes | characteristic |
| 69 | #14556517 | C8 | 1 | 1 | yes | characteristic |
| 70 | #104×C73 | C8 | 1 | 1 | yes | characteristic |
| 71 | #11924040 | — | 2 | 2 | no | — |
| 72 | #11924040 | — | 2 | 2 | no | — |
| 73 | #11924040 | — | 2 | 2 | no | — |
| 74 | #11924040 | C22⋊C4 | 1 | 2 | yes | — |
| 75 | #11924040 | C22⋊C4 | 1 | 2 | yes | — |
| 76 | #11924038 | — | 2 | 1 | no | — |
| 77 | #11924038 | — | 2 | 1 | no | — |
| 78 | #11924038 | C42 | 1 | 1 | yes | characteristic |
| 79 | #11924038 | C42 | 1 | 1 | yes | characteristic |
| 80 | #11924037 | — | 2 | 1 | no | — |
| 81 | #11924037 | — | 2 | 1 | no | — |
| 82 | #11924037 | — | 2 | 1 | no | — |
| 83 | #11924036 | — | 2 | 1 | no | — |
| 84 | #11924036 | — | 2 | 1 | no | — |
| 85 | #11924036 | — | 2 | 1 | no | — |
| 86 | #11924036 | — | 2 | 1 | no | — |
| 87 | #11924036 | C2×C8 | 1 | 2 | yes | — |
| 88 | #11924036 | C22×C4 | 1 | 1 | yes | characteristic |
| 89 | #11924036 | C22×C4 | 1 | 1 | yes | characteristic |
| 90 | #11924036 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | #11924036 | #41 | 1 | 1 | yes | characteristic |
| 92 | C2×#10596833 | — | 2 | 1 | no | — |
| 93 | C2×#10596833 | — | 2 | 1 | no | — |
| 94 | C2×#10596833 | — | 2 | 1 | no | — |
| 95 | C2×#10596833 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C2×#10596833 | #41 | 1 | 1 | yes | characteristic |
| 97 | C4⋊#64408 | C2×C8 | 1 | 2 | yes | — |
| 98 | C22⋊#64408 | — | 2 | 1 | no | — |
| 99 | C4×#64408 | — | 2 | 1 | no | — |
| 100 | #11924029 | C42 | 1 | 1 | yes | characteristic |
| 101 | #11924028 | — | 2 | 1 | no | — |
| 102 | #11924028 | C2×C8 | 1 | 1 | yes | characteristic |
| 103 | #11924027 | — | 2 | 1 | no | — |
| 104 | #11924027 | C42 | 1 | 1 | yes | characteristic |
| 105 | Q8×D73 | C2×C8 | 1 | 1 | yes | characteristic |
| 106 | D4×D73 | — | 2 | 1 | no | — |
| 107 | D4×D73 | C2×C8 | 1 | 1 | yes | characteristic |
| 108 | C2×C4×D73 | — | 2 | 1 | no | — |
| 109 | C2×C4×D73 | — | 2 | 1 | no | — |
| 110 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 111 | #11924012 | C2×C8 | 1 | 1 | yes | characteristic |
| 112 | #11924011 | — | 2 | 1 | no | — |
| 113 | C8×D73 | — | 2 | 1 | no | — |
| 114 | C4×Dic73 | — | 2 | 1 | no | — |
| 115 | C4×Dic73 | C2×C8 | 1 | 1 | yes | characteristic |
| 116 | #41×C73 | C2×C8 | 1 | 1 | yes | characteristic |
| 117 | M16×C73 | C2×C8 | 1 | 1 | yes | characteristic |
| 118 | C42×C73 | C2×C8 | 1 | 1 | yes | characteristic |
| 119 | C22×D73 | — | 2 | 1 | no | — |
| 120 | C22×D73 | #131 | 1 | 1 | yes | characteristic |
| 121 | C2×#64408 | — | 2 | 2 | no | — |
| 122 | Q8×C73 | C4×C8 | 1 | 1 | yes | characteristic |
| 123 | D4×C73 | — | 2 | 1 | no | — |
| 124 | D4×C73 | C4×C8 | 1 | 1 | yes | characteristic |
| 125 | C2×C4×C73 | — | 2 | 1 | no | — |
| 126 | C2×C4×C73 | — | 2 | 1 | no | — |
| 127 | C2×C4×C73 | C22×C8 | 1 | 1 | yes | characteristic |
| 128 | C22⋊D73 | — | 2 | 1 | no | — |
| 129 | C22⋊D73 | — | 2 | 1 | no | — |
| 130 | C22⋊D73 | — | 2 | 1 | no | — |
| 131 | C2×Dic73 | — | 2 | 1 | no | — |
| 132 | C2×Dic73 | — | 2 | 1 | no | — |
| 133 | C2×Dic73 | C4×D4 | 1 | 1 | yes | characteristic |
| 134 | D292 | — | 2 | 1 | no | — |
| 135 | D292 | C4×C8 | 1 | 1 | yes | characteristic |
| 136 | C4×D73 | — | 2 | 1 | no | — |
| 137 | C4×D73 | — | 2 | 1 | no | — |
| 138 | C4×D73 | — | 2 | 1 | no | — |
| 139 | C4×D73 | — | 4 | 2 | no | — |
| 140 | C4×D73 | C2×C42 | 1 | 1 | yes | characteristic |
| 141 | C4×D73 | C4×D4 | 1 | 1 | yes | characteristic |
| 142 | C4×D73 | C22×C8 | 1 | 1 | yes | characteristic |
| 143 | C4×D73 | #131 | 1 | 1 | yes | characteristic |
| 144 | Dic146 | — | 2 | 1 | no | — |
| 145 | Dic146 | C4×C8 | 1 | 1 | yes | characteristic |
| 146 | #10596833 | — | 2 | 1 | no | — |
| 147 | #10596833 | — | 2 | 1 | no | — |
| 148 | #10596833 | — | 2 | 2 | no | — |
| 149 | #10596833 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 150 | #10596833 | #117 | 1 | 1 | yes | characteristic |
| 151 | #10596833 | C4×D4 | 1 | 1 | yes | characteristic |
| 152 | #10596833 | C4×D4 | 1 | 1 | yes | characteristic |
| 153 | C8×C73 | — | 2 | 1 | no | — |
| 154 | #10596831 | — | 2 | 1 | no | — |
| 155 | C22×C73 | — | 2 | 1 | no | — |
| 156 | C22×C73 | C8×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×D73 | — | 2 | 2 | no | — |
| 158 | C2×D73 | — | 2 | 1 | no | — |
| 159 | C2×D73 | — | 4 | 2 | no | — |
| 160 | C2×D73 | #405 | 1 | 1 | yes | characteristic |
| 161 | C2×D73 | C8×D4 | 1 | 1 | yes | characteristic |
| 162 | #64408 | — | 4 | 2 | no | — |
| 163 | C4×C73 | — | 2 | 1 | no | — |
| 164 | C4×C73 | — | 4 | 1 | no | — |
| 165 | C4×C73 | C2×C4×C8 | 1 | 1 | yes | characteristic |
| 166 | C4×C73 | C8×D4 | 1 | 1 | yes | characteristic |
| 167 | Dic73 | — | 2 | 1 | no | — |
| 168 | Dic73 | — | 4 | 1 | no | — |
| 169 | Dic73 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 170 | Dic73 | C8×D4 | 1 | 1 | yes | characteristic |
| 171 | #12615 | — | 73 | 1 | no | maximal, Sylow |
| 172 | C2×C73 | — | 2 | 1 | no | — |
| 173 | C2×C73 | — | 4 | 1 | no | — |
| 174 | C2×C73 | C8×C22⋊C4 | 1 | 1 | yes | characteristic |
| 175 | D73 | — | 2 | 1 | no | — |
| 176 | D73 | — | 4 | 1 | no | — |
| 177 | D73 | #2171 | 1 | 2 | yes | — |
| 178 | C2×#504 | — | 73 | 1 | no | — |
| 179 | C2×#350 | — | 73 | 1 | no | — |
| 180 | #2108 | — | 73 | 1 | no | — |
| 181 | C2×#346 | — | 73 | 1 | no | — |
| 182 | #1764 | — | 73 | 1 | no | — |
| 183 | #1379 | — | 73 | 1 | no | — |
| 184 | #1376 | — | 73 | 1 | no | — |
| 185 | C73 | #12615 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 186 | C2×#131 | — | 73 | 1 | no | — |
| 187 | #504 | — | 73 | 2 | no | — |
| 188 | #504 | — | 73 | 2 | no | — |
| 189 | #504 | — | 146 | 2 | no | — |
| 190 | C2×M32 | — | 73 | 1 | no | — |
| 191 | C2×M32 | — | 73 | 1 | no | — |
| 192 | C2×M32 | — | 146 | 1 | no | — |
| 193 | C22×C16 | — | 73 | 1 | no | — |
| 194 | C22×C16 | — | 73 | 1 | no | — |
| 195 | C22×C16 | — | 146 | 1 | no | — |
| 196 | C2×#104 | — | 73 | 1 | no | — |
| 197 | #416 | — | 73 | 1 | no | — |
| 198 | #405 | — | 73 | 1 | no | — |
| 199 | C2×C4×C8 | — | 73 | 1 | no | — |
| 200 | #350 | — | 73 | 2 | no | — |
| 201 | #350 | — | 73 | 2 | no | — |
| 202 | #346 | — | 146 | 2 | no | — |
| 203 | #346 | — | 146 | 1 | no | — |
| 204 | C4×C16 | — | 146 | 1 | no | — |
| 205 | #341 | — | 73 | 1 | no | — |
| 206 | #339 | — | 73 | 1 | no | — |
| 207 | C2×#41 | — | 73 | 1 | no | — |
| 208 | #131 | — | 73 | 1 | no | — |
| 209 | #131 | — | 73 | 1 | no | — |
| 210 | #131 | — | 73 | 1 | no | — |
| 211 | #131 | — | 73 | 1 | no | — |
| 212 | #131 | — | 146 | 1 | no | — |
| 213 | #131 | — | 146 | 1 | no | — |
| 214 | C2×M16 | — | 73 | 1 | no | — |
| 215 | C2×M16 | — | 73 | 1 | no | — |
| 216 | C2×M16 | — | 146 | 1 | no | — |
| 217 | C22×C8 | — | 73 | 1 | no | — |
| 218 | C22×C8 | — | 73 | 1 | no | — |
| 219 | C22×C8 | — | 146 | 1 | no | — |
| 220 | #117 | — | 73 | 1 | no | — |
| 221 | C2×C42 | — | 73 | 1 | no | — |
| 222 | M32 | — | 73 | 2 | no | — |
| 223 | M32 | — | 73 | 2 | no | — |
| 224 | M32 | — | 146 | 2 | no | — |
| 225 | M32 | — | 146 | 2 | no | — |
| 226 | M32 | — | 146 | 1 | no | — |
| 227 | M32 | — | 146 | 1 | no | — |
| 228 | C2×C16 | — | 73 | 2 | no | — |
| 229 | C2×C16 | — | 73 | 2 | no | — |
| 230 | C2×C16 | — | 73 | 1 | no | — |
| 231 | C2×C16 | — | 73 | 1 | no | — |
| 232 | C2×C16 | — | 73 | 2 | no | — |
| 233 | C2×C16 | — | 146 | 2 | no | — |
| 234 | C2×C16 | — | 146 | 2 | no | — |
| 235 | C2×C16 | — | 146 | 1 | no | — |
| 236 | C2×C16 | — | 146 | 1 | no | — |
| 237 | C2×C16 | — | 146 | 1 | no | — |
| 238 | C2×C16 | — | 146 | 1 | no | — |
| 239 | #104 | — | 73 | 1 | no | — |
| 240 | #104 | — | 73 | 1 | no | — |
| 241 | #104 | — | 73 | 1 | no | — |
| 242 | #104 | #10596842 | 1 | 1 | yes | characteristic |
| 243 | #103 | — | 73 | 2 | no | — |
| 244 | #102 | — | 73 | 2 | no | — |
| 245 | #97 | — | 146 | 1 | no | — |
| 246 | C4×C8 | — | 146 | 1 | no | — |
| 247 | C4×C8 | — | 146 | 1 | no | — |
| 248 | C4×C8 | — | 146 | 1 | no | — |
| 249 | #41 | — | 73 | 1 | no | — |
| 250 | #41 | — | 73 | 1 | no | — |
| 251 | #41 | — | 73 | 1 | no | — |
| 252 | #41 | — | 146 | 1 | no | — |
| 253 | #41 | — | 146 | 1 | no | — |
| 254 | #41 | C2×#10596842 | 1 | 1 | yes | characteristic |
| 255 | C2×Q8 | — | 73 | 1 | no | — |
| 256 | C2×D4 | — | 73 | 1 | no | — |
| 257 | C2×D4 | — | 146 | 1 | no | — |
| 258 | C22×C4 | — | 73 | 1 | no | — |
| 259 | C22×C4 | — | 146 | 1 | no | — |
| 260 | C22×C4 | — | 146 | 1 | no | — |
| 261 | M16 | — | 73 | 1 | no | — |
| 262 | M16 | — | 73 | 1 | no | — |
| 263 | M16 | — | 73 | 1 | no | — |
| 264 | M16 | — | 146 | 1 | no | — |
| 265 | M16 | — | 146 | 1 | no | — |
| 266 | M16 | — | 146 | 1 | no | — |
| 267 | M16 | — | 146 | 1 | no | — |
| 268 | M16 | — | 146 | 1 | no | — |
| 269 | M16 | — | 146 | 1 | no | — |
| 270 | M16 | C2×#10596842 | 1 | 1 | yes | characteristic |
| 271 | C2×C8 | — | 73 | 1 | no | — |
| 272 | C2×C8 | — | 73 | 1 | no | — |
| 273 | C2×C8 | — | 73 | 1 | no | — |
| 274 | C2×C8 | — | 73 | 1 | no | — |
| 275 | C2×C8 | — | 73 | 1 | no | — |
| 276 | C2×C8 | — | 73 | 1 | no | — |
| 277 | C2×C8 | — | 73 | 2 | no | — |
| 278 | C2×C8 | — | 146 | 1 | no | — |
| 279 | C2×C8 | — | 146 | 1 | no | — |
| 280 | C2×C8 | — | 146 | 1 | no | — |
| 281 | C2×C8 | — | 146 | 1 | no | — |
| 282 | C2×C8 | — | 146 | 1 | no | — |
| 283 | C2×C8 | — | 146 | 1 | no | — |
| 284 | C2×C8 | — | 146 | 1 | no | — |
| 285 | C2×C8 | — | 146 | 1 | no | — |
| 286 | C4⋊C4 | — | 73 | 2 | no | — |
| 287 | C22⋊C4 | — | 146 | 1 | no | — |
| 288 | C42 | — | 73 | 1 | no | — |
| 289 | C42 | — | 146 | 1 | no | — |
| 290 | C42 | — | 146 | 1 | no | — |
| 291 | C42 | C2×#10596842 | 1 | 1 | yes | characteristic |
| 292 | C16 | — | 73 | 2 | no | — |
| 293 | C16 | — | 73 | 2 | no | — |
| 294 | C16 | — | 146 | 2 | no | — |
| 295 | C16 | — | 146 | 2 | no | — |
| 296 | C16 | — | 146 | 2 | no | — |
| 297 | C23 | — | 73 | 1 | no | — |
| 298 | C23 | — | 146 | 1 | no | — |
| 299 | Q8 | — | 73 | 1 | no | — |
| 300 | Q8 | — | 146 | 1 | no | — |
| 301 | Q8 | C4×#10596842 | 1 | 1 | yes | characteristic |
| 302 | D4 | — | 2 | 1 | no | — |
| 303 | D4 | — | 73 | 1 | no | — |
| 304 | D4 | — | 146 | 1 | no | — |
| 305 | D4 | — | 146 | 1 | no | — |
| 306 | D4 | — | 146 | 1 | no | — |
| 307 | D4 | — | 146 | 1 | no | — |
| 308 | D4 | C4×#10596842 | 1 | 1 | yes | characteristic |
| 309 | C2×C4 | — | 2 | 1 | no | — |
| 310 | C2×C4 | — | 2 | 1 | no | — |
| 311 | C2×C4 | — | 292 | 2 | no | — |
| 312 | C2×C4 | — | 73 | 1 | no | — |
| 313 | C2×C4 | — | 73 | 1 | no | — |
| 314 | C2×C4 | — | 73 | 1 | no | — |
| 315 | C2×C4 | — | 73 | 1 | no | — |
| 316 | C2×C4 | — | 73 | 1 | no | — |
| 317 | C2×C4 | — | 146 | 1 | no | — |
| 318 | C2×C4 | — | 146 | 1 | no | — |
| 319 | C2×C4 | — | 146 | 2 | no | — |
| 320 | C2×C4 | — | 146 | 1 | no | — |
| 321 | C2×C4 | — | 146 | 1 | no | — |
| 322 | C2×C4 | — | 146 | 1 | no | — |
| 323 | C2×C4 | C22×#10596842 | 1 | 1 | yes | characteristic |
| 324 | C8 | — | 2 | 1 | no | — |
| 325 | C8 | — | 73 | 1 | no | — |
| 326 | C8 | — | 73 | 1 | no | — |
| 327 | C8 | — | 73 | 1 | no | — |
| 328 | C8 | — | 73 | 1 | no | — |
| 329 | C8 | — | 146 | 2 | no | — |
| 330 | C8 | — | 146 | 1 | no | — |
| 331 | C8 | — | 146 | 1 | no | — |
| 332 | C8 | — | 146 | 1 | no | — |
| 333 | C22 | — | 2 | 1 | no | — |
| 334 | C22 | — | 292 | 2 | no | — |
| 335 | C22 | — | 73 | 1 | no | — |
| 336 | C22 | — | 73 | 1 | no | — |
| 337 | C22 | — | 146 | 2 | no | — |
| 338 | C22 | — | 146 | 1 | no | — |
| 339 | C22 | D4×#10596842 | 1 | 1 | yes | characteristic |
| 340 | C4 | — | 2 | 1 | no | — |
| 341 | C4 | — | 4 | 1 | no | — |
| 342 | C4 | — | 292 | 1 | no | — |
| 343 | C4 | — | 292 | 2 | no | — |
| 344 | C4 | — | 73 | 1 | no | — |
| 345 | C4 | — | 73 | 1 | no | — |
| 346 | C4 | — | 146 | 1 | no | — |
| 347 | C4 | C2×C4×#10596842 | 1 | 1 | yes | characteristic |
| 348 | C4 | D4×#10596842 | 1 | 1 | yes | characteristic |
| 349 | C2 | — | 2 | 1 | no | — |
| 350 | C2 | — | 4 | 1 | no | — |
| 351 | C2 | — | 292 | 1 | no | — |
| 352 | C2 | — | 73 | 2 | no | — |
| 353 | C2 | — | 146 | 1 | no | — |
| 354 | C2 | C22⋊C4×#10596842 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta