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. #13125582 | C2 | semidirect |
| 2. #13125552 | C2 | semidirect |
| 4. #13125207 | C2 | semidirect |
| 5. #13114507 | C2 | semidirect |
| 6. #13114488 | C2 | semidirect |
| 7. #13114473 | C2 | semidirect |
| 8. #13114441 | C2 | semidirect |
| 9. #13114438 | C2 | semidirect |
| 10. #13113140 | C2 | semidirect |
| 11. C13×#1715 | C2 | semidirect |
| 16. C13×#498 | C22 | semidirect |
| 18. C13×#492 | C22 | semidirect |
| 23. #11718754 | C22 | semidirect |
| 25. #11718742 | C22 | semidirect |
| 29. #11718731 | C22 | semidirect |
| 34. #11718360 | C22 | semidirect |
| 39. #11718343 | C22 | semidirect |
| 40. C13×#322 | C22 | semidirect |
| 41. #11718046 | C22 | semidirect |
| 42. C8×#1055 | C22 | semidirect |
| 140. #1715 | D13 | semidirect |
| 181. #498 | C2×D13 | semidirect |
| 188. #492 | 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 |
|---|---|
| #13125582 | 2 |
| #13125552 | 2 |
| #13125287 | 2 |
| #13125207 | 2 |
| #13114507 | 2 |
| #13114488 | 2 |
| #13114473 | 2 |
| #13114441 | 2 |
| #13114438 | 2 |
| #13113140 | 2 |
| C13×#1715 | 2 |
| #19749 | 13 |