Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
512 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 125 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. #13125490 | C2 | semidirect |
| 3. #13117056 | C2 | semidirect |
| 4. #13117053 | C2 | semidirect |
| 5. #13117010 | C2 | semidirect |
| 6. #13116915 | C2 | semidirect |
| 8. #13116728 | C2 | semidirect |
| 9. #13116724 | C2 | semidirect |
| 10. #13116649 | C2 | semidirect |
| 23. #11718845 | C22 | semidirect |
| 24. #11718842 | C22 | semidirect |
| 29. #11718519 | C22 | semidirect |
| 30. #11718514 | C22 | semidirect |
| 36. #11718157 | C22 | semidirect |
| 38. #11718109 | C22 | semidirect |
| 39. #11718105 | C22 | semidirect |
| 40. #11718104 | C22 | semidirect |
| 41. #11718103 | C22 | semidirect |
| 42. #11718079 | C22 | semidirect |
| 344. C13 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125490 | 2 |
| #13123739 | 2 |
| #13117056 | 2 |
| #13117053 | 2 |
| #13117010 | 2 |
| #13116915 | 2 |
| #13116787 | 2 |
| #13116728 | 2 |
| #13116724 | 2 |
| #13116649 | 2 |
| C13×#2191 | 2 |
| #33693 | 13 |