Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
526 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14539514 | C2 | semidirect |
| 2. #14537693 | C2 | semidirect |
| 3. #14530998 | C2 | semidirect |
| 4. #14530959 | C2 | semidirect |
| 5. #14530856 | C2 | semidirect |
| 6. #14530734 | C2 | semidirect |
| 8. #14530681 | C2 | semidirect |
| 9. #14530678 | C2 | semidirect |
| 10. #14530593 | C2 | semidirect |
| 11. C17×#2239 | C2 | semidirect |
| 17. #11763209 | C22 | semidirect |
| 18. #11763194 | C22 | semidirect |
| 26. #11762920 | C22 | semidirect |
| 27. #11762916 | C22 | semidirect |
| 31. #11762633 | C22 | semidirect |
| 32. #11762629 | C22 | semidirect |
| 33. #11762621 | C22 | semidirect |
| 37. #11762586 | C22 | semidirect |
| 40. C17×#365 | C22 | semidirect |
| 41. C17×#362 | C22 | semidirect |
| 179. #2239 | D17 | semidirect |
| 227. #365 | C2×D17 | semidirect |
| 229. #362 | C2×D17 | semidirect |
| 288. C17 | #33690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539514 | 2 |
| #14537693 | 2 |
| #14530998 | 2 |
| #14530959 | 2 |
| #14530856 | 2 |
| #14530734 | 2 |
| #14530732 | 2 |
| #14530681 | 2 |
| #14530678 | 2 |
| #14530593 | 2 |
| C17×#2239 | 2 |
| #33690 | 17 |