Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
822 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 159 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. #13125579 | C2 | semidirect |
| 2. #13125556 | C2 | semidirect |
| 4. #13125207 | C2 | semidirect |
| 5. #13114492 | C2 | semidirect |
| 6. #13114477 | C2 | semidirect |
| 7. #13114464 | C2 | semidirect |
| 8. #13114443 | C2 | semidirect |
| 9. #13114435 | C2 | semidirect |
| 10. #13113140 | C2 | semidirect |
| 11. C13×#1722 | C2 | semidirect |
| 16. C13×#500 | C22 | semidirect |
| 17. C13×#494 | C22 | semidirect |
| 23. #11718754 | C22 | semidirect |
| 25. #11718749 | C22 | semidirect |
| 27. #11718742 | C22 | semidirect |
| 36. #11718354 | C22 | semidirect |
| 39. #11718341 | C22 | semidirect |
| 40. C13×#322 | C22 | semidirect |
| 41. #11718046 | C22 | semidirect |
| 42. C8×#1055 | C22 | semidirect |
| 137. #1722 | D13 | semidirect |
| 180. #500 | C2×D13 | semidirect |
| 183. #494 | C2×D13 | semidirect |
| 205. #322 | C2×D13 | semidirect |
| 319. C13 | #19749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125579 | 2 |
| #13125556 | 2 |
| #13125283 | 2 |
| #13125207 | 2 |
| #13114492 | 2 |
| #13114477 | 2 |
| #13114464 | 2 |
| #13114443 | 2 |
| #13114435 | 2 |
| #13113140 | 2 |
| C13×#1722 | 2 |
| #19749 | 13 |