Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
788 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 163 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. #14539736 | C2 | semidirect |
| 2. #14539702 | C2 | semidirect |
| 3. #14539522 | C2 | semidirect |
| 4. #14528452 | C2 | semidirect |
| 5. #14528446 | C2 | semidirect |
| 6. #14528424 | C2 | semidirect |
| 7. #14528388 | C2 | semidirect |
| 8. #14527081 | C2 | semidirect |
| 9. C17×#3138 | C2 | semidirect |
| 11. #11763207 | C22 | semidirect |
| 12. #11763188 | C22 | semidirect |
| 13. #11763186 | C22 | semidirect |
| 16. #11763183 | C22 | semidirect |
| 17. #11763161 | C22 | semidirect |
| 18. #11763157 | C22 | semidirect |
| 19. #11763156 | C22 | semidirect |
| 29. #11762531 | C22 | semidirect |
| 30. #11762530 | C22 | semidirect |
| 31. C8×#3622 | C22 | semidirect |
| 152. #3138 | D17 | semidirect |
| 248. C17 | #19729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539736 | 2 |
| #14539702 | 2 |
| #14539522 | 2 |
| #14528452 | 2 |
| #14528446 | 2 |
| #14528424 | 2 |
| #14528388 | 2 |
| #14527081 | 2 |
| C17×#3138 | 2 |
| #19729 | 17 |