Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1502 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 331 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×#11718376 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | C2×#11718373 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C2×#11718357 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C2×#11718354 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #13120946 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13120942 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C13×#1726 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×Dic52 | C22 | 1 | 3 | yes | — |
| 9 | C22×D104 | C22 | 1 | 3 | yes | — |
| 10 | C22×#6095 | C22 | 1 | 3 | yes | — |
| 11 | C22×#6095 | C22 | 1 | 6 | yes | — |
| 12 | C22×#6095 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#88129 | C22 | 1 | 3 | yes | — |
| 14 | C2×#88129 | C22 | 1 | 3 | yes | — |
| 15 | C2×#88128 | C22 | 1 | 3 | yes | — |
| 16 | C2×#88123 | C22 | 1 | 3 | yes | — |
| 17 | C2×C13×#97 | C22 | 1 | 3 | yes | — |
| 18 | C2×C4×C8×C13 | C22 | 1 | 3 | yes | — |
| 19 | C13×#376 | C22 | 1 | 1 | yes | characteristic |
| 20 | #11718376 | — | 2 | 12 | no | — |
| 21 | #11718373 | — | 2 | 12 | no | — |
| 22 | #11718357 | — | 2 | 12 | no | — |
| 23 | #11718354 | — | 2 | 12 | no | — |
| 24 | #11718338 | — | 2 | 4 | no | — |
| 25 | #11718332 | — | 2 | 4 | no | — |
| 26 | C22×D52 | — | 2 | 6 | no | — |
| 27 | C22×D52 | C23 | 1 | 3 | yes | — |
| 28 | C22×D52 | C23 | 1 | 1 | yes | characteristic |
| 29 | C22×Dic26 | C23 | 1 | 3 | yes | — |
| 30 | C22×Dic26 | C23 | 1 | 1 | yes | characteristic |
| 31 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 32 | C22×C8×C13 | C23 | 1 | 3 | yes | — |
| 33 | C2×C42×C13 | C23 | 1 | 3 | yes | — |
| 34 | C2×#6103 | — | 2 | 6 | no | — |
| 35 | C2×#6103 | — | 2 | 6 | no | — |
| 36 | C2×C4⋊Dic13 | — | 2 | 6 | no | — |
| 37 | C2×Dic52 | — | 2 | 6 | no | — |
| 38 | C2×Dic52 | — | 2 | 12 | no | — |
| 39 | C2×D104 | — | 2 | 6 | no | — |
| 40 | C2×D104 | — | 2 | 12 | no | — |
| 41 | C2×#6095 | — | 2 | 12 | no | — |
| 42 | C2×#6095 | — | 2 | 12 | no | — |
| 43 | C2×#6095 | — | 2 | 6 | no | — |
| 44 | C2×#6095 | — | 2 | 6 | no | — |
| 45 | C2×#6095 | — | 2 | 12 | no | — |
| 46 | C2×#6095 | — | 2 | 12 | no | — |
| 47 | #88129 | — | 2 | 6 | no | — |
| 48 | #88129 | — | 2 | 6 | no | — |
| 49 | #88129 | — | 2 | 6 | no | — |
| 50 | #88129 | — | 2 | 6 | no | — |
| 51 | #88128 | — | 2 | 6 | no | — |
| 52 | #88128 | — | 2 | 6 | no | — |
| 53 | #88123 | — | 2 | 6 | no | — |
| 54 | #88123 | — | 2 | 6 | no | — |
| 55 | C13×#97 | D4 | 1 | 12 | yes | complemented |
| 56 | C4×C8×C13 | D4 | 1 | 12 | yes | complemented |
| 57 | C13×#95 | D4 | 1 | 4 | yes | — |
| 58 | #33307 | — | 13 | 1 | no | maximal, Sylow |
| 59 | C23×D13 | — | 2 | 1 | no | — |
| 60 | C23×D13 | — | 2 | 3 | no | — |
| 61 | C22×C4×C13 | C2×D4 | 1 | 6 | yes | — |
| 62 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 63 | C22×Dic13 | — | 2 | 3 | no | — |
| 64 | C22×Dic13 | — | 2 | 1 | no | — |
| 65 | C2×D52 | — | 2 | 6 | no | — |
| 66 | C2×D52 | — | 2 | 6 | no | — |
| 67 | C2×D52 | — | 2 | 3 | no | — |
| 68 | C2×D52 | — | 2 | 3 | no | — |
| 69 | C2×D52 | — | 2 | 3 | no | — |
| 70 | C2×D52 | — | 2 | 3 | no | — |
| 71 | C2×D52 | — | 4 | 12 | no | — |
| 72 | C2×D52 | — | 8 | 12 | no | — |
| 73 | C2×Dic26 | — | 2 | 6 | no | — |
| 74 | C2×Dic26 | — | 2 | 6 | no | — |
| 75 | C2×Dic26 | — | 2 | 3 | no | — |
| 76 | C2×Dic26 | — | 2 | 3 | no | — |
| 77 | C2×Dic26 | — | 2 | 3 | no | — |
| 78 | C2×Dic26 | — | 2 | 3 | no | — |
| 79 | C2×C8×C13 | C2×D4 | 1 | 6 | yes | — |
| 80 | C2×C8×C13 | C2×D4 | 1 | 6 | yes | — |
| 81 | C2×C8×C13 | C2×D4 | 1 | 12 | yes | — |
| 82 | C42×C13 | C2×D4 | 1 | 6 | yes | — |
| 83 | C42×C13 | C2×D4 | 1 | 6 | yes | — |
| 84 | #6103 | — | 4 | 12 | no | — |
| 85 | #6103 | — | 4 | 12 | no | — |
| 86 | C4⋊Dic13 | — | 4 | 12 | no | — |
| 87 | Dic52 | — | 4 | 12 | no | — |
| 88 | D104 | — | 4 | 12 | no | — |
| 89 | #6095 | — | 4 | 12 | no | — |
| 90 | #6095 | — | 4 | 4 | no | — |
| 91 | #6095 | — | 4 | 24 | no | — |
| 92 | C2×#497 | — | 13 | 3 | no | — |
| 93 | C2×#496 | — | 13 | 3 | no | — |
| 94 | C2×#495 | — | 13 | 3 | no | — |
| 95 | C2×#492 | — | 13 | 3 | no | — |
| 96 | #2658 | — | 13 | 1 | no | — |
| 97 | #2657 | — | 13 | 1 | no | — |
| 98 | #1726 | D13 | 1 | 1 | yes | characteristic, complemented |
| 99 | C23×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 100 | C22×D13 | — | 4 | 3 | no | — |
| 101 | C22×D13 | — | 4 | 3 | no | — |
| 102 | C22×D13 | — | 4 | 6 | no | — |
| 103 | C22×D13 | — | 4 | 12 | no | — |
| 104 | C22×D13 | — | 4 | 4 | no | — |
| 105 | C2×C4×C13 | — | 2 | 12 | no | — |
| 106 | C2×C4×C13 | #127 | 1 | 12 | yes | — |
| 107 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 108 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 109 | C2×Dic13 | — | 4 | 6 | no | — |
| 110 | C2×Dic13 | — | 4 | 3 | no | — |
| 111 | C2×Dic13 | — | 4 | 3 | no | — |
| 112 | D52 | — | 4 | 3 | no | — |
| 113 | D52 | — | 4 | 6 | no | — |
| 114 | D52 | — | 4 | 1 | no | — |
| 115 | D52 | — | 4 | 3 | no | — |
| 116 | D52 | — | 4 | 3 | no | — |
| 117 | D52 | — | 8 | 24 | no | — |
| 118 | Dic26 | — | 4 | 3 | no | — |
| 119 | Dic26 | — | 4 | 6 | no | — |
| 120 | Dic26 | — | 4 | 1 | no | — |
| 121 | Dic26 | — | 4 | 3 | no | — |
| 122 | Dic26 | — | 4 | 3 | no | — |
| 123 | C8×C13 | #127 | 1 | 4 | yes | — |
| 124 | C8×C13 | #127 | 1 | 12 | yes | — |
| 125 | C22×Q16 | — | 13 | 3 | no | — |
| 126 | C22×SD16 | — | 13 | 3 | no | — |
| 127 | C22×SD16 | — | 13 | 6 | no | — |
| 128 | C22×SD16 | — | 13 | 1 | no | — |
| 129 | C22×D8 | — | 13 | 3 | no | — |
| 130 | C2×C4⋊Q8 | — | 13 | 3 | no | — |
| 131 | C2×#127 | — | 13 | 3 | no | — |
| 132 | C2×#124 | — | 13 | 3 | no | — |
| 133 | C2×#124 | — | 13 | 3 | no | — |
| 134 | #497 | — | 26 | 12 | no | — |
| 135 | #496 | — | 26 | 12 | no | — |
| 136 | #495 | — | 26 | 12 | no | — |
| 137 | #492 | — | 26 | 12 | no | — |
| 138 | C2×#97 | C2×D13 | 1 | 3 | yes | — |
| 139 | C2×C4×C8 | C2×D13 | 1 | 3 | yes | — |
| 140 | #399 | — | 26 | 4 | no | — |
| 141 | #392 | — | 26 | 4 | no | — |
| 142 | #376 | C2×D13 | 1 | 1 | yes | characteristic |
| 143 | C22×C13 | C2×#127 | 1 | 3 | yes | — |
| 144 | C22×C13 | #577 | 1 | 4 | yes | — |
| 145 | C2×D13 | — | 8 | 3 | no | — |
| 146 | C2×D13 | — | 8 | 1 | no | — |
| 147 | C2×D13 | — | 8 | 12 | no | — |
| 148 | C2×D13 | — | 8 | 6 | no | — |
| 149 | C2×D13 | — | 8 | 6 | no | — |
| 150 | C4×C13 | — | 2 | 12 | no | — |
| 151 | C4×C13 | C2×#127 | 1 | 1 | yes | characteristic |
| 152 | C4×C13 | C2×#127 | 1 | 3 | yes | — |
| 153 | Dic13 | — | 8 | 3 | no | — |
| 154 | Dic13 | — | 8 | 1 | no | — |
| 155 | C22×Q8 | — | 13 | 1 | no | — |
| 156 | C22×Q8 | — | 13 | 3 | no | — |
| 157 | C22×D4 | — | 13 | 1 | no | — |
| 158 | C22×D4 | — | 13 | 3 | no | — |
| 159 | C22×D4 | — | 26 | 6 | no | — |
| 160 | C2×Q16 | — | 26 | 6 | no | — |
| 161 | C2×Q16 | — | 26 | 12 | no | — |
| 162 | C2×SD16 | — | 26 | 12 | no | — |
| 163 | C2×SD16 | — | 26 | 12 | no | — |
| 164 | C2×SD16 | — | 26 | 6 | no | — |
| 165 | C2×SD16 | — | 26 | 6 | no | — |
| 166 | C2×SD16 | — | 26 | 12 | no | — |
| 167 | C2×SD16 | — | 26 | 12 | no | — |
| 168 | C2×D8 | — | 26 | 6 | no | — |
| 169 | C2×D8 | — | 26 | 12 | no | — |
| 170 | C22×C8 | C22×D13 | 1 | 3 | yes | — |
| 171 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 172 | C4⋊Q8 | — | 26 | 6 | no | — |
| 173 | C4⋊Q8 | — | 26 | 6 | no | — |
| 174 | #127 | — | 26 | 6 | no | — |
| 175 | #127 | — | 26 | 6 | no | — |
| 176 | #124 | — | 26 | 6 | no | — |
| 177 | #124 | — | 26 | 6 | no | — |
| 178 | #124 | — | 26 | 6 | no | — |
| 179 | #124 | — | 26 | 6 | no | — |
| 180 | C2×C4⋊C4 | — | 26 | 6 | no | — |
| 181 | C2×C22⋊C4 | — | 26 | 6 | no | — |
| 182 | C2×C22⋊C4 | — | 26 | 6 | no | — |
| 183 | C2×C42 | C22×D13 | 1 | 3 | yes | — |
| 184 | #97 | D52 | 1 | 12 | yes | complemented |
| 185 | C4×C8 | D52 | 1 | 12 | yes | complemented |
| 186 | #95 | D52 | 1 | 4 | yes | — |
| 187 | C2×C13 | #2867 | 1 | 1 | yes | characteristic |
| 188 | C2×C13 | #3154 | 1 | 6 | yes | — |
| 189 | D13 | — | 16 | 3 | no | — |
| 190 | D13 | — | 16 | 1 | no | — |
| 191 | C24 | — | 26 | 1 | no | — |
| 192 | C24 | — | 26 | 3 | no | — |
| 193 | C2×Q8 | — | 26 | 3 | no | — |
| 194 | C2×Q8 | — | 26 | 3 | no | — |
| 195 | C2×Q8 | — | 26 | 3 | no | — |
| 196 | C2×Q8 | — | 26 | 3 | no | — |
| 197 | C2×Q8 | — | 26 | 6 | no | — |
| 198 | C2×Q8 | — | 26 | 6 | no | — |
| 199 | C2×D4 | — | 26 | 3 | no | — |
| 200 | C2×D4 | — | 26 | 3 | no | — |
| 201 | C2×D4 | — | 26 | 3 | no | — |
| 202 | C2×D4 | — | 26 | 3 | no | — |
| 203 | C2×D4 | — | 26 | 6 | no | — |
| 204 | C2×D4 | — | 26 | 6 | no | — |
| 205 | C2×D4 | — | 52 | 12 | no | — |
| 206 | C2×D4 | — | 104 | 12 | no | — |
| 207 | C22×C4 | — | 26 | 1 | no | — |
| 208 | C22×C4 | — | 26 | 3 | no | — |
| 209 | C22×C4 | C2×D52 | 1 | 6 | yes | — |
| 210 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 211 | Q16 | — | 52 | 12 | no | — |
| 212 | SD16 | — | 52 | 24 | no | — |
| 213 | SD16 | — | 52 | 12 | no | — |
| 214 | SD16 | — | 52 | 4 | no | — |
| 215 | D8 | — | 52 | 12 | no | — |
| 216 | C2×C8 | C2×D52 | 1 | 6 | yes | — |
| 217 | C2×C8 | C2×D52 | 1 | 6 | yes | — |
| 218 | C2×C8 | C2×D52 | 1 | 12 | yes | — |
| 219 | C4⋊C4 | — | 52 | 12 | no | — |
| 220 | C22⋊C4 | — | 52 | 12 | no | — |
| 221 | C22⋊C4 | — | 52 | 12 | no | — |
| 222 | C42 | C2×D52 | 1 | 6 | yes | — |
| 223 | C42 | C2×D52 | 1 | 6 | yes | — |
| 224 | C13 | #33307 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 225 | C23 | — | 52 | 3 | no | — |
| 226 | C23 | — | 52 | 3 | no | — |
| 227 | C23 | — | 52 | 6 | no | — |
| 228 | C23 | — | 52 | 12 | no | — |
| 229 | C23 | — | 52 | 4 | no | — |
| 230 | C23 | C22×D52 | 1 | 1 | yes | characteristic |
| 231 | Q8 | — | 52 | 6 | no | — |
| 232 | Q8 | — | 52 | 1 | no | — |
| 233 | Q8 | — | 52 | 3 | no | — |
| 234 | Q8 | — | 52 | 3 | no | — |
| 235 | Q8 | — | 52 | 3 | no | — |
| 236 | D4 | — | 52 | 3 | no | — |
| 237 | D4 | — | 52 | 3 | no | — |
| 238 | D4 | — | 52 | 1 | no | — |
| 239 | D4 | — | 52 | 3 | no | — |
| 240 | D4 | — | 52 | 6 | no | — |
| 241 | D4 | — | 104 | 24 | no | — |
| 242 | C2×C4 | — | 2 | 12 | no | — |
| 243 | C2×C4 | — | 52 | 3 | no | — |
| 244 | C2×C4 | — | 52 | 3 | no | — |
| 245 | C2×C4 | — | 52 | 6 | no | — |
| 246 | C2×C4 | #88128 | 1 | 12 | yes | — |
| 247 | C2×C4 | C22×D52 | 1 | 3 | yes | — |
| 248 | C2×C4 | C22×D52 | 1 | 3 | yes | — |
| 249 | C8 | #88128 | 1 | 12 | yes | — |
| 250 | C8 | #88128 | 1 | 4 | yes | — |
| 251 | C22 | — | 104 | 1 | no | — |
| 252 | C22 | — | 104 | 3 | no | — |
| 253 | C22 | — | 104 | 12 | no | — |
| 254 | C22 | — | 104 | 6 | no | — |
| 255 | C22 | — | 104 | 6 | no | — |
| 256 | C22 | C2×#88128 | 1 | 3 | yes | — |
| 257 | C22 | #11719456 | 1 | 4 | yes | — |
| 258 | C4 | — | 2 | 12 | no | — |
| 259 | C4 | — | 104 | 1 | no | — |
| 260 | C4 | — | 104 | 3 | no | — |
| 261 | C4 | C2×#88128 | 1 | 3 | yes | — |
| 262 | C4 | C2×#88128 | 1 | 1 | yes | characteristic |
| 263 | C2 | — | 208 | 3 | no | — |
| 264 | C2 | — | 208 | 1 | no | — |
| 265 | C2 | #13123231 | 1 | 1 | yes | characteristic |
| 266 | C2 | #13125312 | 1 | 6 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11718376 | C2 | semidirect |
| 2. C2×#11718373 | C2 | semidirect |
| 3. C2×#11718357 | C2 | semidirect |
| 4. C2×#11718354 | C2 | semidirect |
| 5. #13120946 | C2 | semidirect |
| 6. #13120942 | C2 | semidirect |
| 7. C13×#1726 | C2 | semidirect |
| 55. C13×#97 | D4 | semidirect |
| 56. C4×C8×C13 | D4 | semidirect |
| 98. #1726 | D13 | semidirect |
| 184. #97 | D52 | semidirect |
| 185. C4×C8 | D52 | semidirect |
| 224. C13 | #33307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718376 | 2 |
| C2×#11718373 | 2 |
| C2×#11718357 | 2 |
| C2×#11718354 | 2 |
| #13120946 | 2 |
| #13120942 | 2 |
| C13×#1726 | 2 |
| #33307 | 13 |