Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
512 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14539440 | C2 | semidirect |
| 3. #14531002 | C2 | semidirect |
| 4. #14530961 | C2 | semidirect |
| 5. #14530960 | C2 | semidirect |
| 6. #14530862 | C2 | semidirect |
| 8. #14530678 | C2 | semidirect |
| 9. #14530676 | C2 | semidirect |
| 10. #14530599 | C2 | semidirect |
| 11. C17×#2214 | C2 | semidirect |
| 16. #11763211 | C22 | semidirect |
| 25. #11762916 | C22 | semidirect |
| 30. #11762633 | C22 | semidirect |
| 31. #11762632 | C22 | semidirect |
| 32. #11762630 | C22 | semidirect |
| 33. #11762625 | C22 | semidirect |
| 37. #11762586 | C22 | semidirect |
| 39. C17×#494 | C22 | semidirect |
| 41. C17×#364 | C22 | semidirect |
| 42. C17×#362 | C22 | semidirect |
| 193. #2214 | D17 | semidirect |
| 219. #494 | C2×D17 | semidirect |
| 237. #364 | C2×D17 | semidirect |
| 239. #362 | C2×D17 | semidirect |
| 298. C17 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539440 | 2 |
| #14537682 | 2 |
| #14531002 | 2 |
| #14530961 | 2 |
| #14530960 | 2 |
| #14530862 | 2 |
| #14530733 | 2 |
| #14530678 | 2 |
| #14530676 | 2 |
| #14530599 | 2 |
| C17×#2214 | 2 |
| #33693 | 17 |