Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
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. #14539527 | C2 | semidirect |
| 2. #14539504 | C2 | semidirect |
| 4. #14539155 | C2 | semidirect |
| 5. #14528440 | C2 | semidirect |
| 6. #14528425 | C2 | semidirect |
| 7. #14528412 | C2 | semidirect |
| 8. #14528391 | C2 | semidirect |
| 9. #14528383 | C2 | semidirect |
| 10. #14527088 | C2 | semidirect |
| 11. C17×#1722 | C2 | semidirect |
| 16. #11763207 | C22 | semidirect |
| 21. #11763182 | C22 | semidirect |
| 23. #11763161 | C22 | semidirect |
| 24. #11763159 | C22 | semidirect |
| 26. #11763157 | C22 | semidirect |
| 36. #11762531 | C22 | semidirect |
| 37. C8×#3622 | C22 | semidirect |
| 38. C17×#500 | C22 | semidirect |
| 39. C17×#494 | C22 | semidirect |
| 42. C17×#322 | C22 | semidirect |
| 169. #1722 | D17 | semidirect |
| 197. #500 | C2×D17 | semidirect |
| 200. #494 | C2×D17 | semidirect |
| 222. #322 | C2×D17 | semidirect |
| 275. C17 | #19749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539527 | 2 |
| #14539504 | 2 |
| #14539231 | 2 |
| #14539155 | 2 |
| #14528440 | 2 |
| #14528425 | 2 |
| #14528412 | 2 |
| #14528391 | 2 |
| #14528383 | 2 |
| #14527088 | 2 |
| C17×#1722 | 2 |
| #19749 | 17 |