Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
910 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 910 conjugacy classes of subgroups — too many to draw. Only its 139 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 | #13129530 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13125850 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #13114135 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #13114132 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #13114125 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13113464 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C13×#1655 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C13×H(3,𝔽4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | D13×#127 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | #11719385 | C22 | 1 | 3 | yes | — |
| 11 | #11719377 | C22 | 1 | 3 | yes | complemented |
| 12 | #11719376 | — | 2 | 3 | no | — |
| 13 | #11719374 | — | 2 | 3 | no | — |
| 14 | #11719298 | — | 2 | 3 | no | — |
| 15 | #11719292 | — | 2 | 3 | no | — |
| 16 | C13×#496 | C22 | 1 | 3 | yes | — |
| 17 | #11718830 | — | 2 | 3 | no | — |
| 18 | #11718824 | — | 2 | 3 | no | — |
| 19 | #11718817 | — | 2 | 3 | no | — |
| 20 | #11718811 | — | 2 | 3 | no | — |
| 21 | #11718732 | C22 | 1 | 3 | yes | complemented |
| 22 | #11718719 | C22 | 1 | 3 | yes | — |
| 23 | #11718374 | C22 | 1 | 3 | yes | complemented |
| 24 | #11718366 | C22 | 1 | 3 | yes | complemented |
| 25 | C13×#329 | C22 | 1 | 3 | yes | complemented |
| 26 | #11718132 | C22 | 1 | 3 | yes | complemented |
| 27 | #11718057 | C22 | 1 | 6 | yes | complemented |
| 28 | C2×D4×D13 | — | 2 | 3 | no | — |
| 29 | C2×C13×SD16 | — | 2 | 3 | no | — |
| 30 | C2×C13×D8 | — | 2 | 3 | no | — |
| 31 | C13×#127 | C23 | 1 | 1 | yes | characteristic |
| 32 | C13×#124 | — | 2 | 3 | no | — |
| 33 | C13×#124 | C23 | 1 | 3 | yes | — |
| 34 | C13×#120 | — | 2 | 3 | no | — |
| 35 | #88207 | — | 2 | 1 | no | — |
| 36 | C2×C22⋊Dic13 | — | 2 | 3 | no | — |
| 37 | #88200 | D4 | 1 | 3 | yes | — |
| 38 | Q8×Dic13 | D4 | 1 | 3 | yes | — |
| 39 | #88198 | — | 2 | 3 | no | — |
| 40 | C2×#6106 | — | 2 | 3 | no | — |
| 41 | #88194 | — | 2 | 3 | no | — |
| 42 | #88193 | — | 2 | 3 | no | — |
| 43 | #88192 | D4 | 1 | 3 | yes | — |
| 44 | #88190 | — | 2 | 3 | no | — |
| 45 | #88189 | — | 2 | 3 | no | — |
| 46 | #88189 | — | 2 | 3 | no | — |
| 47 | D4×Dic13 | — | 2 | 3 | no | — |
| 48 | D4×Dic13 | D4 | 1 | 3 | yes | — |
| 49 | C2×#6104 | — | 2 | 3 | no | — |
| 50 | #88139 | — | 2 | 3 | no | — |
| 51 | #88137 | — | 2 | 3 | no | — |
| 52 | #88135 | — | 2 | 3 | no | — |
| 53 | #88133 | — | 2 | 3 | no | — |
| 54 | #88133 | — | 2 | 3 | no | — |
| 55 | #88133 | — | 2 | 3 | no | — |
| 56 | #88133 | — | 2 | 3 | no | — |
| 57 | #88132 | — | 2 | 3 | no | — |
| 58 | #88132 | — | 2 | 3 | no | — |
| 59 | #88132 | — | 2 | 3 | no | — |
| 60 | #88131 | — | 2 | 3 | no | — |
| 61 | #88131 | — | 2 | 3 | no | — |
| 62 | #88130 | — | 2 | 1 | no | — |
| 63 | #88128 | C23 | 1 | 1 | yes | characteristic |
| 64 | C42×D13 | C23 | 1 | 1 | yes | characteristic |
| 65 | #88124 | C23 | 1 | 3 | yes | — |
| 66 | C4×Dic26 | — | 2 | 3 | no | — |
| 67 | C13×#97 | C23 | 1 | 3 | yes | — |
| 68 | #88072 | — | 2 | 3 | no | — |
| 69 | #88072 | — | 2 | 3 | no | — |
| 70 | #88061 | — | 2 | 3 | no | — |
| 71 | #88061 | — | 2 | 3 | no | — |
| 72 | #88060 | — | 2 | 3 | no | — |
| 73 | #88054 | — | 2 | 3 | no | — |
| 74 | #88043 | C23 | 1 | 3 | yes | — |
| 75 | #19094 | — | 13 | 1 | no | maximal, Sylow |
| 76 | C24×C13 | — | 2 | 1 | no | — |
| 77 | C23×D13 | — | 4 | 1 | no | — |
| 78 | C2×Q8×C13 | C2×D4 | 1 | 3 | yes | — |
| 79 | C2×D4×C13 | — | 2 | 3 | no | — |
| 80 | C2×D4×C13 | — | 2 | 3 | no | — |
| 81 | C2×D4×C13 | C2×D4 | 1 | 3 | yes | — |
| 82 | C2×C22⋊D13 | — | 2 | 3 | no | — |
| 83 | C2×C22⋊D13 | — | 4 | 3 | no | — |
| 84 | C22×Dic13 | — | 2 | 3 | no | — |
| 85 | C22×Dic13 | — | 2 | 3 | no | — |
| 86 | D4×D13 | — | 8 | 3 | no | — |
| 87 | D4×D13 | — | 8 | 3 | no | — |
| 88 | C2×D52 | — | 2 | 3 | no | — |
| 89 | C2×C4×D13 | C2×D4 | 1 | 3 | yes | — |
| 90 | C2×Dic26 | — | 2 | 3 | no | — |
| 91 | C13×SD16 | — | 8 | 3 | no | — |
| 92 | C13×D8 | — | 8 | 3 | no | — |
| 93 | C2×C8×C13 | — | 2 | 3 | no | — |
| 94 | C13×C22⋊C4 | — | 2 | 3 | no | — |
| 95 | C13×C22⋊C4 | — | 2 | 3 | no | — |
| 96 | C13×C22⋊C4 | — | 2 | 3 | no | — |
| 97 | C42×C13 | — | 2 | 1 | no | — |
| 98 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 99 | C22⋊Dic13 | — | 2 | 3 | no | — |
| 100 | C22⋊Dic13 | — | 2 | 3 | no | — |
| 101 | C22⋊Dic13 | — | 2 | 3 | no | — |
| 102 | C22⋊Dic13 | — | 2 | 3 | no | — |
| 103 | C22⋊Dic13 | — | 2 | 3 | no | — |
| 104 | #6106 | — | 8 | 3 | no | — |
| 105 | #6104 | — | 8 | 3 | no | — |
| 106 | #6103 | — | 2 | 3 | no | — |
| 107 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 108 | C4⋊Dic13 | C2×D4 | 1 | 3 | yes | — |
| 109 | C4⋊Dic13 | C2×D4 | 1 | 3 | yes | — |
| 110 | #6101 | — | 2 | 3 | no | — |
| 111 | #6101 | — | 2 | 3 | no | — |
| 112 | #6101 | — | 2 | 3 | no | — |
| 113 | #6101 | — | 2 | 3 | no | — |
| 114 | #6101 | — | 2 | 3 | no | — |
| 115 | C4×Dic13 | — | 2 | 3 | no | — |
| 116 | C4×Dic13 | — | 2 | 3 | no | — |
| 117 | C4×Dic13 | C2×D4 | 1 | 3 | yes | — |
| 118 | C2×#1055 | — | 2 | 3 | no | — |
| 119 | #3568 | — | 13 | 1 | no | — |
| 120 | #3217 | — | 13 | 3 | no | — |
| 121 | #1657 | — | 13 | 3 | no | — |
| 122 | #1657 | — | 13 | 3 | no | — |
| 123 | #1655 | — | 13 | 1 | no | — |
| 124 | #1655 | D13 | 1 | 1 | yes | characteristic, complemented |
| 125 | #1535 | — | 13 | 3 | no | — |
| 126 | C23×C13 | — | 2 | 3 | no | — |
| 127 | C23×C13 | — | 4 | 1 | no | — |
| 128 | C23×C13 | — | 8 | 3 | no | — |
| 129 | C22×D13 | — | 4 | 1 | no | — |
| 130 | C22×D13 | — | 8 | 6 | no | — |
| 131 | C22×D13 | #120 | 1 | 1 | yes | characteristic |
| 132 | Q8×C13 | — | 4 | 3 | no | — |
| 133 | D4×C13 | — | 4 | 3 | no | — |
| 134 | D4×C13 | — | 4 | 3 | no | — |
| 135 | D4×C13 | — | 4 | 3 | no | — |
| 136 | D4×C13 | — | 8 | 3 | no | — |
| 137 | C2×C4×C13 | — | 2 | 3 | no | — |
| 138 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 139 | C22⋊D13 | — | 8 | 6 | no | — |
| 140 | C22⋊D13 | — | 8 | 3 | no | — |
| 141 | C2×Dic13 | — | 2 | 3 | no | — |
| 142 | C2×Dic13 | — | 2 | 3 | no | — |
| 143 | C2×Dic13 | — | 8 | 3 | no | — |
| 144 | C2×Dic13 | — | 8 | 3 | no | — |
| 145 | C2×Dic13 | #120 | 1 | 3 | yes | — |
| 146 | D52 | — | 4 | 3 | no | — |
| 147 | D52 | — | 4 | 3 | no | — |
| 148 | C4×D13 | — | 4 | 3 | no | — |
| 149 | Dic26 | — | 8 | 3 | no | — |
| 150 | C8×C13 | — | 4 | 3 | no | — |
| 151 | #1055 | — | 4 | 3 | no | — |
| 152 | #563 | — | 13 | 3 | no | — |
| 153 | H(3,𝔽4) | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 154 | #556 | — | 26 | 3 | no | — |
| 155 | #551 | — | 26 | 3 | no | — |
| 156 | #542 | — | 26 | 3 | no | — |
| 157 | #538 | — | 26 | 3 | no | — |
| 158 | C2×#127 | — | 13 | 1 | no | — |
| 159 | #529 | — | 13 | 3 | no | — |
| 160 | #496 | — | 13 | 3 | no | — |
| 161 | #496 | C2×D13 | 1 | 3 | yes | — |
| 162 | #490 | — | 13 | 3 | no | — |
| 163 | #490 | — | 13 | 3 | no | — |
| 164 | #460 | — | 26 | 3 | no | — |
| 165 | #459 | — | 26 | 3 | no | — |
| 166 | #450 | — | 26 | 3 | no | — |
| 167 | #447 | — | 26 | 3 | no | — |
| 168 | #432 | — | 13 | 3 | no | — |
| 169 | #330 | — | 13 | 6 | no | — |
| 170 | #329 | — | 13 | 3 | no | — |
| 171 | #329 | C2×D13 | 1 | 3 | yes | complemented |
| 172 | C22×C13 | — | 4 | 3 | no | — |
| 173 | C22×C13 | — | 4 | 3 | no | — |
| 174 | C22×C13 | — | 4 | 3 | no | — |
| 175 | C22×C13 | — | 8 | 3 | no | — |
| 176 | C22×C13 | — | 16 | 2 | no | — |
| 177 | C22×C13 | C2×#120 | 1 | 1 | yes | characteristic |
| 178 | C2×D13 | — | 2 | 3 | no | — |
| 179 | C2×D13 | — | 8 | 3 | no | — |
| 180 | C2×D13 | — | 16 | 4 | no | — |
| 181 | C4×C13 | — | 2 | 3 | no | — |
| 182 | C4×C13 | — | 4 | 3 | no | — |
| 183 | Dic13 | — | 2 | 3 | no | — |
| 184 | Dic13 | — | 4 | 3 | no | — |
| 185 | Dic13 | — | 4 | 3 | no | — |
| 186 | C22×D4 | — | 26 | 3 | no | — |
| 187 | C2×SD16 | — | 2 | 3 | no | — |
| 188 | C2×SD16 | — | 26 | 3 | no | — |
| 189 | C2×D8 | — | 2 | 3 | no | — |
| 190 | C2×D8 | — | 26 | 3 | no | — |
| 191 | C4⋊Q8 | — | 26 | 3 | no | — |
| 192 | #127 | — | 13 | 1 | no | — |
| 193 | #127 | — | 26 | 3 | no | — |
| 194 | #127 | C22×D13 | 1 | 1 | yes | characteristic |
| 195 | #126 | — | 26 | 1 | no | — |
| 196 | #126 | — | 26 | 3 | no | — |
| 197 | #126 | — | 26 | 3 | no | — |
| 198 | #126 | — | 26 | 3 | no | — |
| 199 | #126 | — | 26 | 3 | no | — |
| 200 | #125 | — | 13 | 3 | no | — |
| 201 | #124 | — | 2 | 3 | no | — |
| 202 | #124 | — | 26 | 3 | no | — |
| 203 | #124 | — | 26 | 3 | no | — |
| 204 | #124 | C22×D13 | 1 | 3 | yes | — |
| 205 | #123 | — | 26 | 3 | no | — |
| 206 | #123 | — | 26 | 3 | no | — |
| 207 | #123 | — | 26 | 3 | no | — |
| 208 | C22⋊Q8 | — | 13 | 3 | no | — |
| 209 | C22⋊Q8 | — | 26 | 3 | no | — |
| 210 | C22⋊Q8 | — | 26 | 3 | no | — |
| 211 | C22⋊Q8 | — | 26 | 3 | no | — |
| 212 | #121 | — | 13 | 3 | no | — |
| 213 | #121 | — | 26 | 3 | no | — |
| 214 | #120 | — | 2 | 3 | no | — |
| 215 | #120 | — | 26 | 1 | no | — |
| 216 | C4×Q8 | — | 13 | 3 | no | — |
| 217 | C4×Q8 | — | 26 | 3 | no | — |
| 218 | C4×D4 | — | 13 | 3 | no | — |
| 219 | C4×D4 | — | 26 | 3 | no | — |
| 220 | C4×D4 | — | 26 | 3 | no | — |
| 221 | #117 | — | 26 | 3 | no | — |
| 222 | #117 | — | 26 | 3 | no | — |
| 223 | C2×C22⋊C4 | — | 26 | 3 | no | — |
| 224 | C2×C42 | — | 13 | 1 | no | — |
| 225 | C4⋊C8 | — | 26 | 3 | no | — |
| 226 | #102 | — | 26 | 3 | no | — |
| 227 | #102 | — | 26 | 3 | no | — |
| 228 | #102 | — | 26 | 3 | no | — |
| 229 | #102 | — | 26 | 3 | no | — |
| 230 | C22⋊C8 | — | 26 | 3 | no | — |
| 231 | #97 | — | 13 | 3 | no | — |
| 232 | #97 | C22×D13 | 1 | 3 | yes | — |
| 233 | C2×C13 | — | 8 | 3 | no | — |
| 234 | C2×C13 | — | 16 | 1 | no | — |
| 235 | C2×C13 | #3021 | 1 | 3 | yes | — |
| 236 | D13 | — | 4 | 1 | no | — |
| 237 | D13 | — | 16 | 1 | no | — |
| 238 | C24 | — | 2 | 1 | no | — |
| 239 | C24 | — | 52 | 1 | no | — |
| 240 | C2×Q8 | — | 26 | 3 | no | — |
| 241 | C2×Q8 | D4×D13 | 1 | 3 | yes | — |
| 242 | C2×D4 | — | 2 | 3 | no | — |
| 243 | C2×D4 | — | 2 | 3 | no | — |
| 244 | C2×D4 | — | 26 | 3 | no | — |
| 245 | C2×D4 | — | 26 | 3 | no | — |
| 246 | C2×D4 | — | 52 | 3 | no | — |
| 247 | C2×D4 | — | 104 | 3 | no | — |
| 248 | C2×D4 | — | 104 | 3 | no | — |
| 249 | C2×D4 | D4×D13 | 1 | 3 | yes | — |
| 250 | C22×C4 | — | 13 | 3 | no | — |
| 251 | C22×C4 | — | 26 | 3 | no | — |
| 252 | C22×C4 | — | 26 | 3 | no | — |
| 253 | SD16 | — | 8 | 3 | no | — |
| 254 | SD16 | — | 104 | 3 | no | — |
| 255 | D8 | — | 8 | 3 | no | — |
| 256 | D8 | — | 104 | 3 | no | — |
| 257 | C2×C8 | — | 2 | 3 | no | — |
| 258 | C2×C8 | — | 26 | 3 | no | — |
| 259 | C4⋊C4 | — | 13 | 3 | no | — |
| 260 | C4⋊C4 | — | 13 | 3 | no | — |
| 261 | C4⋊C4 | — | 26 | 3 | no | — |
| 262 | C4⋊C4 | — | 26 | 3 | no | — |
| 263 | C4⋊C4 | — | 26 | 3 | no | — |
| 264 | C4⋊C4 | — | 26 | 3 | no | — |
| 265 | C4⋊C4 | — | 26 | 3 | no | — |
| 266 | C4⋊C4 | — | 26 | 3 | no | — |
| 267 | C22⋊C4 | — | 2 | 3 | no | — |
| 268 | C22⋊C4 | — | 2 | 3 | no | — |
| 269 | C22⋊C4 | — | 2 | 3 | no | — |
| 270 | C22⋊C4 | — | 26 | 3 | no | — |
| 271 | C22⋊C4 | — | 26 | 3 | no | — |
| 272 | C22⋊C4 | — | 26 | 3 | no | — |
| 273 | C22⋊C4 | — | 26 | 3 | no | — |
| 274 | C22⋊C4 | — | 26 | 3 | no | — |
| 275 | C22⋊C4 | — | 26 | 3 | no | — |
| 276 | C42 | — | 2 | 1 | no | — |
| 277 | C42 | — | 13 | 3 | no | — |
| 278 | C42 | — | 26 | 3 | no | — |
| 279 | C42 | — | 26 | 3 | no | — |
| 280 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 281 | C13 | #19094 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 282 | C23 | — | 2 | 3 | no | — |
| 283 | C23 | — | 4 | 1 | no | — |
| 284 | C23 | — | 8 | 3 | no | — |
| 285 | C23 | — | 13 | 1 | no | — |
| 286 | C23 | — | 52 | 1 | no | — |
| 287 | C23 | — | 104 | 6 | no | — |
| 288 | Q8 | — | 4 | 3 | no | — |
| 289 | Q8 | — | 104 | 3 | no | — |
| 290 | D4 | — | 4 | 3 | no | — |
| 291 | D4 | — | 4 | 3 | no | — |
| 292 | D4 | — | 4 | 3 | no | — |
| 293 | D4 | — | 8 | 3 | no | — |
| 294 | D4 | — | 52 | 3 | no | — |
| 295 | D4 | — | 52 | 3 | no | — |
| 296 | D4 | — | 104 | 6 | no | — |
| 297 | D4 | — | 104 | 3 | no | — |
| 298 | C2×C4 | — | 2 | 3 | no | — |
| 299 | C2×C4 | — | 13 | 3 | no | — |
| 300 | C2×C4 | — | 26 | 3 | no | — |
| 301 | C2×C4 | — | 26 | 3 | no | — |
| 302 | C2×C4 | — | 52 | 3 | no | — |
| 303 | C2×C4 | — | 104 | 3 | no | — |
| 304 | C2×C4 | — | 104 | 3 | no | — |
| 305 | C2×C4 | C2×D4×D13 | 1 | 3 | yes | — |
| 306 | C8 | — | 4 | 3 | no | — |
| 307 | C8 | — | 52 | 3 | no | — |
| 308 | C22 | — | 4 | 3 | no | — |
| 309 | C22 | — | 4 | 3 | no | — |
| 310 | C22 | — | 4 | 3 | no | — |
| 311 | C22 | — | 8 | 3 | no | — |
| 312 | C22 | — | 16 | 2 | no | — |
| 313 | C22 | — | 26 | 3 | no | — |
| 314 | C22 | — | 104 | 3 | no | — |
| 315 | C22 | — | 208 | 4 | no | — |
| 316 | C22 | D13×#120 | 1 | 1 | yes | characteristic |
| 317 | C4 | — | 2 | 3 | no | — |
| 318 | C4 | — | 4 | 3 | no | — |
| 319 | C4 | — | 26 | 3 | no | — |
| 320 | C4 | — | 52 | 3 | no | — |
| 321 | C4 | — | 52 | 3 | no | — |
| 322 | C2 | — | 8 | 3 | no | — |
| 323 | C2 | — | 16 | 1 | no | — |
| 324 | C2 | — | 52 | 1 | no | — |
| 325 | C2 | — | 208 | 1 | no | — |
| 326 | C2 | #13124204 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13129530 | C2 | semidirect |
| 2. #13125850 | C2 | semidirect |
| 3. #13114135 | C2 | semidirect |
| 4. #13114132 | C2 | semidirect |
| 5. #13114125 | C2 | semidirect |
| 6. #13113464 | C2 | semidirect |
| 7. C13×#1655 | C2 | semidirect |
| 8. C13×H(3,𝔽4) | C22 | semidirect |
| 9. D13×#127 | C22 | semidirect |
| 11. #11719377 | C22 | semidirect |
| 21. #11718732 | C22 | semidirect |
| 23. #11718374 | C22 | semidirect |
| 24. #11718366 | C22 | semidirect |
| 25. C13×#329 | C22 | semidirect |
| 26. #11718132 | C22 | semidirect |
| 27. #11718057 | C22 | semidirect |
| 124. #1655 | D13 | semidirect |
| 153. H(3,𝔽4) | C2×D13 | semidirect |
| 171. #329 | C2×D13 | semidirect |
| 281. C13 | #19094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129530 | 2 |
| #13125850 | 2 |
| #13114135 | 2 |
| #13114132 | 2 |
| #13114125 | 2 |
| #13113464 | 2 |
| C13×#1655 | 2 |
| #19094 | 13 |