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. #13125557 | C2 | semidirect |
| 4. #13125207 | C2 | semidirect |
| 5. #13114505 | C2 | semidirect |
| 6. #13114490 | C2 | semidirect |
| 7. #13114476 | C2 | semidirect |
| 8. #13114465 | C2 | semidirect |
| 9. #13114442 | C2 | semidirect |
| 10. #13113138 | C2 | semidirect |
| 11. C13×#1708 | C2 | semidirect |
| 16. C13×#498 | C22 | semidirect |
| 18. C13×#487 | C22 | semidirect |
| 21. #11718754 | C22 | semidirect |
| 24. #11718746 | C22 | semidirect |
| 25. #11718739 | C22 | semidirect |
| 34. #11718360 | C22 | semidirect |
| 37. #11718355 | C22 | semidirect |
| 40. C82×C13 | C22 | semidirect |
| 41. #11718047 | C22 | semidirect |
| 42. #11718047 | C22 | semidirect |
| 142. #1708 | D13 | semidirect |
| 181. #498 | C2×D13 | semidirect |
| 191. #487 | C2×D13 | semidirect |
| 206. C82 | 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 |
| #13125557 | 2 |
| #13125283 | 2 |
| #13125207 | 2 |
| #13114505 | 2 |
| #13114490 | 2 |
| #13114476 | 2 |
| #13114465 | 2 |
| #13114442 | 2 |
| #13113138 | 2 |
| C13×#1708 | 2 |
| #19749 | 13 |