Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
524 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14539402 | C2 | semidirect |
| 2. #14537687 | C2 | semidirect |
| 3. #14531001 | C2 | semidirect |
| 4. #14530999 | C2 | semidirect |
| 5. #14530953 | C2 | semidirect |
| 6. #14530855 | C2 | semidirect |
| 8. #14530679 | C2 | semidirect |
| 9. #14530676 | C2 | semidirect |
| 10. #14530597 | C2 | semidirect |
| 11. C17×#2191 | C2 | semidirect |
| 15. #11763206 | C22 | semidirect |
| 16. #11763194 | C22 | semidirect |
| 24. #11762920 | C22 | semidirect |
| 25. #11762916 | C22 | semidirect |
| 30. #11762632 | C22 | semidirect |
| 31. #11762631 | C22 | semidirect |
| 32. #11762629 | C22 | semidirect |
| 33. #11762625 | C22 | semidirect |
| 34. #11762623 | C22 | semidirect |
| 37. #11762586 | C22 | semidirect |
| 188. #2191 | D17 | semidirect |
| 295. C17 | #33691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539402 | 2 |
| #14537687 | 2 |
| #14531001 | 2 |
| #14530999 | 2 |
| #14530953 | 2 |
| #14530855 | 2 |
| #14530730 | 2 |
| #14530679 | 2 |
| #14530676 | 2 |
| #14530597 | 2 |
| C17×#2191 | 2 |
| #33691 | 17 |