← #27538816
Subgroups — #27538816
Order 13568.
534 conjugacy classes of subgroups.
The subgroup lattice has 348 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20285251 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20283591 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #20276881 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20276870 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20276860 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20276855 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20276503 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#16810450 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #20276475 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #20276422 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C53×#2139 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #16811254 | — | 2 | 1 | no | — |
| 13 | #16811106 | — | 2 | 1 | no | — |
| 14 | C22×#11719908 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16811031 | — | 2 | 2 | no | — |
| 16 | #16811027 | C22 | 1 | 2 | yes | — |
| 17 | #16811024 | C22 | 1 | 2 | yes | — |
| 18 | #16810724 | — | 2 | 2 | no | — |
| 19 | Q16×Dic53 | C22 | 1 | 2 | yes | — |
| 20 | D8×Dic53 | C22 | 1 | 2 | yes | — |
| 21 | #16810663 | — | 2 | 1 | no | — |
| 22 | #16810661 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#13133151 | C22 | 1 | 1 | yes | characteristic |
| 24 | #16810624 | — | 2 | 1 | no | — |
| 25 | #16810578 | C22 | 1 | 1 | yes | characteristic |
| 26 | #16810451 | C22 | 1 | 2 | yes | — |
| 27 | #16810450 | C22 | 1 | 2 | yes | — |
| 28 | #16810450 | C22 | 1 | 2 | yes | — |
| 29 | #16810449 | C22 | 1 | 2 | yes | — |
| 30 | #16810441 | C22 | 1 | 2 | yes | — |
| 31 | #16810441 | C22 | 1 | 2 | yes | — |
| 32 | #16810427 | C22 | 1 | 1 | yes | characteristic |
| 33 | #16810427 | C22 | 1 | 1 | yes | characteristic |
| 34 | #16810424 | C22 | 1 | 1 | yes | characteristic |
| 35 | #16810424 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#135×C53 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×M32×C53 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#107×C53 | C22 | 1 | 1 | yes | characteristic |
| 39 | C53×#358 | C22 | 1 | 2 | yes | — |
| 40 | C53×#357 | C22 | 1 | 2 | yes | — |
| 41 | C2×#11719917 | D4 | 1 | 1 | yes | characteristic |
| 42 | #13133216 | — | 2 | 2 | no | — |
| 43 | #13133216 | — | 4 | 1 | no | — |
| 44 | #13133208 | — | 2 | 2 | no | — |
| 45 | #13133208 | — | 4 | 1 | no | — |
| 46 | #13133196 | — | 4 | 2 | no | — |
| 47 | Q8×Dic53 | — | 2 | 2 | no | — |
| 48 | D4×Dic53 | — | 2 | 2 | no | — |
| 49 | D4×Dic53 | — | 4 | 2 | no | — |
| 50 | #13133176 | — | 2 | 1 | no | — |
| 51 | #13133176 | — | 4 | 1 | no | — |
| 52 | #13133176 | D4 | 1 | 1 | yes | characteristic |
| 53 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 54 | C2×C4⋊Dic53 | — | 4 | 1 | no | — |
| 55 | C2×#11719908 | — | 2 | 2 | no | — |
| 56 | C2×#11719908 | C23 | 1 | 1 | yes | characteristic |
| 57 | C2×#11719908 | C23 | 1 | 1 | yes | characteristic |
| 58 | #13133151 | — | 2 | 1 | no | — |
| 59 | #13133151 | C23 | 1 | 1 | yes | characteristic |
| 60 | #13133151 | C23 | 1 | 1 | yes | characteristic |
| 61 | #13133151 | C23 | 1 | 2 | yes | — |
| 62 | #13133150 | — | 2 | 2 | no | — |
| 63 | #13133149 | — | 2 | 1 | no | — |
| 64 | #13133148 | — | 2 | 2 | no | — |
| 65 | #13133141 | — | 2 | 2 | no | — |
| 66 | #13133138 | — | 2 | 2 | no | — |
| 67 | #13133127 | D4 | 1 | 2 | yes | — |
| 68 | C8×Dic53 | C23 | 1 | 2 | yes | — |
| 69 | C2×#41×C53 | — | 2 | 1 | no | — |
| 70 | #135×C53 | — | 2 | 2 | no | — |
| 71 | #135×C53 | Q8 | 1 | 4 | yes | complemented |
| 72 | C2×Q16×C53 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 74 | C2×D8×C53 | C23 | 1 | 1 | yes | characteristic |
| 75 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 77 | M32×C53 | — | 2 | 2 | no | — |
| 78 | C2×C16×C53 | C23 | 1 | 2 | yes | — |
| 79 | #107×C53 | — | 2 | 1 | no | — |
| 80 | #107×C53 | C23 | 1 | 2 | yes | — |
| 81 | #41×C53 | — | 2 | 4 | no | — |
| 82 | #41×C53 | — | 4 | 2 | no | — |
| 83 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 84 | C2×D4×C53 | — | 2 | 1 | no | — |
| 85 | C2×D4×C53 | — | 4 | 1 | no | — |
| 86 | C22×C4×C53 | — | 4 | 1 | no | — |
| 87 | C22×C4×C53 | — | 4 | 1 | no | — |
| 88 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C22×Dic53 | — | 4 | 1 | no | — |
| 90 | C22×Dic53 | — | 4 | 2 | no | — |
| 91 | C2×Dic106 | — | 4 | 2 | no | — |
| 92 | Q16×C53 | — | 2 | 1 | no | — |
| 93 | Q16×C53 | C2×Q8 | 1 | 2 | yes | — |
| 94 | SD16×C53 | — | 2 | 4 | no | — |
| 95 | D8×C53 | — | 2 | 1 | no | — |
| 96 | D8×C53 | C2×Q8 | 1 | 2 | yes | — |
| 97 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C2×C8×C53 | C2×Q8 | 1 | 2 | yes | — |
| 99 | C2×C8×C53 | #41 | 1 | 2 | yes | — |
| 100 | C2×C8×C53 | C24 | 1 | 1 | yes | characteristic |
| 101 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 102 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 103 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 104 | C22⋊Dic53 | — | 4 | 2 | no | — |
| 105 | C22⋊Dic53 | D8 | 1 | 2 | yes | — |
| 106 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 107 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 108 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 109 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 110 | C4⋊Dic53 | — | 4 | 2 | no | — |
| 111 | C4⋊Dic53 | — | 4 | 2 | no | — |
| 112 | C4⋊Dic53 | D8 | 1 | 1 | yes | characteristic |
| 113 | C4⋊Dic53 | D8 | 1 | 1 | yes | characteristic |
| 114 | #11719919 | — | 4 | 2 | no | — |
| 115 | #11719919 | — | 4 | 2 | no | — |
| 116 | C4×Dic53 | — | 4 | 1 | no | — |
| 117 | C4×Dic53 | — | 4 | 2 | no | — |
| 118 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 119 | #11719917 | — | 2 | 2 | no | — |
| 120 | C2×#88322 | C2×D4 | 1 | 2 | yes | — |
| 121 | C16×C53 | — | 2 | 2 | no | — |
| 122 | #11719908 | — | 2 | 1 | no | — |
| 123 | #11719908 | — | 2 | 1 | no | — |
| 124 | C23×C53 | — | 4 | 1 | no | — |
| 125 | C23×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 126 | Q8×C53 | — | 2 | 2 | no | — |
| 127 | Q8×C53 | — | 4 | 1 | no | — |
| 128 | D4×C53 | — | 2 | 2 | no | — |
| 129 | D4×C53 | — | 4 | 4 | no | — |
| 130 | D4×C53 | — | 4 | 1 | no | — |
| 131 | C2×C4×C53 | — | 4 | 1 | no | — |
| 132 | C2×C4×C53 | — | 4 | 4 | no | — |
| 133 | C2×C4×C53 | — | 4 | 2 | no | — |
| 134 | C2×C4×C53 | — | 16 | 1 | no | — |
| 135 | C2×C4×C53 | C22⋊Q8 | 1 | 2 | yes | — |
| 136 | C2×C4×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×C53 | #137 | 1 | 2 | yes | — |
| 138 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×Dic53 | — | 4 | 1 | no | — |
| 140 | C2×Dic53 | — | 4 | 2 | no | — |
| 141 | C2×Dic53 | — | 4 | 1 | no | — |
| 142 | C2×Dic53 | — | 16 | 2 | no | — |
| 143 | C2×Dic53 | — | 16 | 1 | no | — |
| 144 | C2×Dic53 | C2×D8 | 1 | 2 | yes | — |
| 145 | C2×Dic53 | C2×D8 | 1 | 2 | yes | — |
| 146 | Dic106 | — | 16 | 2 | no | — |
| 147 | C8×C53 | C22⋊Q8 | 1 | 2 | yes | — |
| 148 | C8×C53 | C22×Q8 | 1 | 1 | yes | characteristic |
| 149 | C8×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 150 | #88322 | — | 2 | 2 | no | — |
| 151 | #33634 | — | 53 | 1 | no | maximal, Sylow |
| 152 | C22×C53 | — | 2 | 1 | no | — |
| 153 | C22×C53 | — | 2 | 1 | no | — |
| 154 | C22×C53 | — | 4 | 2 | no | — |
| 155 | C22×C53 | — | 8 | 1 | no | — |
| 156 | C22×C53 | — | 8 | 1 | no | — |
| 157 | C22×C53 | #474 | 1 | 2 | yes | — |
| 158 | C22×C53 | C22×D8 | 1 | 1 | yes | characteristic |
| 159 | C4×C53 | — | 4 | 2 | no | — |
| 160 | C4×C53 | — | 8 | 2 | no | — |
| 161 | C4×C53 | #474 | 1 | 2 | yes | — |
| 162 | C4×C53 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 163 | C4×C53 | C2×#137 | 1 | 1 | yes | characteristic |
| 164 | Dic53 | — | 2 | 2 | no | — |
| 165 | Dic53 | — | 2 | 2 | no | — |
| 166 | Dic53 | — | 8 | 1 | no | — |
| 167 | Dic53 | — | 8 | 1 | no | — |
| 168 | Dic53 | — | 8 | 2 | no | — |
| 169 | #3164 | — | 53 | 1 | no | — |
| 170 | #2951 | — | 53 | 1 | no | — |
| 171 | #2229 | — | 53 | 2 | no | — |
| 172 | #2228 | — | 53 | 2 | no | — |
| 173 | #2226 | — | 53 | 2 | no | — |
| 174 | #2225 | — | 53 | 2 | no | — |
| 175 | #2159 | — | 53 | 1 | no | — |
| 176 | C2×#367 | — | 53 | 1 | no | — |
| 177 | #2151 | — | 53 | 1 | no | — |
| 178 | #2139 | D53 | 1 | 1 | yes | characteristic |
| 179 | #2138 | — | 53 | 1 | no | — |
| 180 | C2×C53 | — | 2 | 2 | no | — |
| 181 | C2×C53 | — | 8 | 2 | no | — |
| 182 | C2×C53 | C2×#474 | 1 | 1 | yes | characteristic |
| 183 | C2×C53 | #3416 | 1 | 1 | yes | characteristic |
| 184 | C2×C53 | #3416 | 1 | 1 | yes | characteristic |
| 185 | C2×#135 | C2×D53 | 1 | 1 | yes | characteristic |
| 186 | #544 | — | 106 | 1 | no | — |
| 187 | #520 | — | 106 | 1 | no | — |
| 188 | C2×M32 | C2×D53 | 1 | 1 | yes | characteristic |
| 189 | C22×C16 | — | 53 | 1 | no | — |
| 190 | #501 | — | 106 | 2 | no | — |
| 191 | #500 | — | 53 | 2 | no | — |
| 192 | #499 | — | 53 | 2 | no | — |
| 193 | #440 | — | 106 | 2 | no | — |
| 194 | C4×Q16 | — | 53 | 2 | no | — |
| 195 | C4×D8 | — | 53 | 2 | no | — |
| 196 | #428 | — | 106 | 1 | no | — |
| 197 | #427 | — | 53 | 1 | no | — |
| 198 | C2×#107 | — | 53 | 1 | no | — |
| 199 | C2×#107 | C2×D53 | 1 | 1 | yes | characteristic |
| 200 | #417 | — | 106 | 1 | no | — |
| 201 | #405 | — | 53 | 1 | no | — |
| 202 | #367 | — | 53 | 2 | no | — |
| 203 | #367 | — | 53 | 2 | no | — |
| 204 | #367 | — | 53 | 2 | no | — |
| 205 | #366 | — | 53 | 2 | no | — |
| 206 | C4⋊C16 | — | 53 | 2 | no | — |
| 207 | C4⋊C16 | — | 53 | 2 | no | — |
| 208 | #358 | — | 53 | 1 | no | — |
| 209 | #358 | — | 53 | 1 | no | — |
| 210 | #358 | C2×D53 | 1 | 2 | yes | — |
| 211 | #357 | — | 53 | 1 | no | — |
| 212 | #357 | — | 53 | 1 | no | — |
| 213 | #357 | C2×D53 | 1 | 2 | yes | — |
| 214 | C53 | #33634 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 215 | C2×#41 | — | 2 | 1 | no | — |
| 216 | #135 | — | 2 | 2 | no | — |
| 217 | #135 | Dic106 | 1 | 4 | yes | complemented |
| 218 | C2×Q16 | C22×D53 | 1 | 1 | yes | characteristic |
| 219 | C2×SD16 | — | 2 | 1 | no | — |
| 220 | C2×D8 | C22×D53 | 1 | 1 | yes | characteristic |
| 221 | C2×M16 | — | 53 | 1 | no | — |
| 222 | C22×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 223 | C4⋊Q8 | — | 106 | 2 | no | — |
| 224 | C4⋊Q8 | — | 212 | 1 | no | — |
| 225 | #125 | — | 106 | 2 | no | — |
| 226 | #125 | — | 212 | 1 | no | — |
| 227 | C22⋊Q8 | — | 212 | 2 | no | — |
| 228 | C4×Q8 | — | 106 | 2 | no | — |
| 229 | C4×D4 | — | 106 | 2 | no | — |
| 230 | C4×D4 | — | 212 | 2 | no | — |
| 231 | #117 | — | 53 | 1 | no | — |
| 232 | #117 | — | 106 | 1 | no | — |
| 233 | #117 | — | 212 | 1 | no | — |
| 234 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 235 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 236 | C2×C4⋊C4 | — | 212 | 1 | no | — |
| 237 | M32 | — | 2 | 2 | no | — |
| 238 | C2×C16 | — | 53 | 1 | no | — |
| 239 | C2×C16 | — | 53 | 1 | no | — |
| 240 | C2×C16 | — | 106 | 2 | no | — |
| 241 | C2×C16 | C22×D53 | 1 | 2 | yes | — |
| 242 | #107 | — | 2 | 1 | no | — |
| 243 | #107 | — | 53 | 1 | no | — |
| 244 | #107 | — | 53 | 1 | no | — |
| 245 | #107 | — | 53 | 2 | no | — |
| 246 | #107 | — | 106 | 2 | no | — |
| 247 | #107 | — | 106 | 1 | no | — |
| 248 | #107 | C22×D53 | 1 | 2 | yes | — |
| 249 | #106 | — | 106 | 2 | no | — |
| 250 | #106 | — | 106 | 1 | no | — |
| 251 | #103 | — | 106 | 2 | no | — |
| 252 | #102 | — | 106 | 2 | no | — |
| 253 | #97 | — | 53 | 2 | no | — |
| 254 | C4×C8 | — | 53 | 2 | no | — |
| 255 | #41 | — | 2 | 4 | no | — |
| 256 | #41 | — | 4 | 2 | no | — |
| 257 | C2×Q8 | — | 2 | 1 | no | — |
| 258 | C2×Q8 | — | 212 | 2 | no | — |
| 259 | C2×D4 | — | 2 | 1 | no | — |
| 260 | C2×D4 | — | 4 | 1 | no | — |
| 261 | C22×C4 | — | 4 | 1 | no | — |
| 262 | C22×C4 | — | 4 | 1 | no | — |
| 263 | C22×C4 | — | 212 | 2 | no | — |
| 264 | C22×C4 | — | 212 | 1 | no | — |
| 265 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 266 | Q16 | — | 2 | 1 | no | — |
| 267 | Q16 | C2×Dic106 | 1 | 2 | yes | — |
| 268 | SD16 | — | 2 | 4 | no | — |
| 269 | D8 | — | 2 | 1 | no | — |
| 270 | D8 | C2×Dic106 | 1 | 2 | yes | — |
| 271 | M16 | — | 106 | 2 | no | — |
| 272 | C2×C8 | — | 53 | 2 | no | — |
| 273 | C2×C8 | C2×Dic106 | 1 | 2 | yes | — |
| 274 | C2×C8 | D4×D53 | 1 | 1 | yes | characteristic |
| 275 | C2×C8 | #11719947 | 1 | 2 | yes | — |
| 276 | C2×C8 | C23×D53 | 1 | 1 | yes | characteristic |
| 277 | C4⋊C4 | — | 2 | 2 | no | — |
| 278 | C4⋊C4 | — | 4 | 1 | no | — |
| 279 | C4⋊C4 | — | 53 | 1 | no | — |
| 280 | C4⋊C4 | — | 53 | 1 | no | — |
| 281 | C4⋊C4 | — | 106 | 2 | no | — |
| 282 | C4⋊C4 | — | 106 | 1 | no | — |
| 283 | C4⋊C4 | — | 106 | 1 | no | — |
| 284 | C4⋊C4 | — | 212 | 2 | no | — |
| 285 | C4⋊C4 | — | 212 | 2 | no | — |
| 286 | C4⋊C4 | — | 212 | 2 | no | — |
| 287 | C4⋊C4 | — | 212 | 2 | no | — |
| 288 | C4⋊C4 | — | 212 | 1 | no | — |
| 289 | C22⋊C4 | — | 53 | 2 | no | — |
| 290 | C22⋊C4 | — | 212 | 2 | no | — |
| 291 | C22⋊C4 | — | 212 | 1 | no | — |
| 292 | C42 | — | 53 | 2 | no | — |
| 293 | C42 | — | 212 | 2 | no | — |
| 294 | C42 | — | 212 | 1 | no | — |
| 295 | C16 | — | 2 | 2 | no | — |
| 296 | C16 | — | 106 | 1 | no | — |
| 297 | C16 | — | 106 | 1 | no | — |
| 298 | C23 | — | 4 | 1 | no | — |
| 299 | C23 | D8×D53 | 1 | 1 | yes | characteristic |
| 300 | Q8 | — | 2 | 2 | no | — |
| 301 | Q8 | — | 4 | 1 | no | — |
| 302 | Q8 | — | 848 | 2 | no | — |
| 303 | D4 | — | 2 | 2 | no | — |
| 304 | D4 | — | 4 | 4 | no | — |
| 305 | D4 | — | 4 | 1 | no | — |
| 306 | C2×C4 | — | 4 | 1 | no | — |
| 307 | C2×C4 | — | 4 | 4 | no | — |
| 308 | C2×C4 | — | 4 | 2 | no | — |
| 309 | C2×C4 | — | 16 | 1 | no | — |
| 310 | C2×C4 | — | 53 | 2 | no | — |
| 311 | C2×C4 | — | 53 | 2 | no | — |
| 312 | C2×C4 | — | 848 | 2 | no | — |
| 313 | C2×C4 | — | 848 | 1 | no | — |
| 314 | C2×C4 | — | 212 | 1 | no | — |
| 315 | C2×C4 | — | 212 | 2 | no | — |
| 316 | C2×C4 | — | 212 | 1 | no | — |
| 317 | C2×C4 | #13133194 | 1 | 2 | yes | — |
| 318 | C2×C4 | D8×D53 | 1 | 1 | yes | characteristic |
| 319 | C2×C4 | #13133246 | 1 | 2 | yes | — |
| 320 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 321 | C8 | — | 106 | 2 | no | — |
| 322 | C8 | #13133194 | 1 | 2 | yes | — |
| 323 | C8 | C22×Dic106 | 1 | 1 | yes | characteristic |
| 324 | C8 | C2×#11719947 | 1 | 1 | yes | characteristic |
| 325 | C22 | — | 2 | 1 | no | — |
| 326 | C22 | — | 2 | 1 | no | — |
| 327 | C22 | — | 4 | 2 | no | — |
| 328 | C22 | — | 8 | 1 | no | — |
| 329 | C22 | — | 8 | 1 | no | — |
| 330 | C22 | #16810901 | 1 | 2 | yes | — |
| 331 | C22 | C2×D8×D53 | 1 | 1 | yes | characteristic |
| 332 | C4 | — | 4 | 2 | no | — |
| 333 | C4 | — | 8 | 2 | no | — |
| 334 | C4 | — | 106 | 2 | no | — |
| 335 | C4 | — | 106 | 2 | no | — |
| 336 | C4 | — | 424 | 2 | no | — |
| 337 | C4 | — | 424 | 1 | no | — |
| 338 | C4 | — | 424 | 1 | no | — |
| 339 | C4 | #16810901 | 1 | 2 | yes | — |
| 340 | C4 | C2×#13133194 | 1 | 1 | yes | characteristic |
| 341 | C4 | C2×#13133246 | 1 | 1 | yes | characteristic |
| 342 | C2 | — | 2 | 2 | no | — |
| 343 | C2 | — | 8 | 2 | no | — |
| 344 | C2 | C2×#16810901 | 1 | 1 | yes | characteristic |
| 345 | C2 | #20287860 | 1 | 1 | yes | characteristic |
| 346 | C2 | #20287861 | 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