Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
492 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13131490 | C2 | semidirect |
| 2. #13131158 | C2 | semidirect |
| 3. C2×#11718279 | C2 | semidirect |
| 4. #13131079 | C2 | semidirect |
| 5. #13129916 | C2 | semidirect |
| 6. #13129902 | C2 | semidirect |
| 20. C13×#473 | C4 | semidirect |
| 22. #11718853 | C4 | semidirect |
| 23. #11718803 | C4 | semidirect |
| 24. #11718558 | C4 | semidirect |
| 43. C2×C13×Q16 | C2×C4 | semidirect |
| 63. C2×D104 | C2×C4 | semidirect |
| 81. C13×#108 | C2×C4 | semidirect |
| 87. #88059 | C2×C4 | semidirect |
| 217. #473 | #261 | semidirect |
| 268. C2×Q16 | C2×#261 | semidirect |
| 297. #108 | C2×#261 | semidirect |
| 384. C13 | #13005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131490 | 2 |
| #13131158 | 2 |
| C2×#11718279 | 2 |
| #13131079 | 2 |
| #13129916 | 2 |
| #13129902 | 2 |
| #13124558 | 2 |
| #13005 | 13 |