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. #14539444 | C2 | semidirect |
| 3. #14531005 | C2 | semidirect |
| 4. #14530957 | C2 | semidirect |
| 5. #14530866 | C2 | semidirect |
| 6. #14530865 | C2 | semidirect |
| 8. #14530674 | C2 | semidirect |
| 9. #14530672 | C2 | semidirect |
| 10. #14530599 | C2 | semidirect |
| 11. C17×#2231 | C2 | semidirect |
| 17. #11763189 | C22 | semidirect |
| 26. #11762915 | C22 | semidirect |
| 31. #11762631 | C22 | semidirect |
| 32. #11762630 | C22 | semidirect |
| 33. #11762626 | C22 | semidirect |
| 34. #11762624 | C22 | semidirect |
| 37. #11762586 | C22 | semidirect |
| 38. C17×#499 | C22 | semidirect |
| 40. C17×#365 | C22 | semidirect |
| 41. C17×#364 | C22 | semidirect |
| 191. #2231 | D17 | semidirect |
| 218. #499 | C2×D17 | semidirect |
| 235. #365 | C2×D17 | semidirect |
| 237. #364 | 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 |
|---|---|
| #14539444 | 2 |
| #14537682 | 2 |
| #14531005 | 2 |
| #14530957 | 2 |
| #14530866 | 2 |
| #14530865 | 2 |
| #14530736 | 2 |
| #14530674 | 2 |
| #14530672 | 2 |
| #14530599 | 2 |
| C17×#2231 | 2 |
| #33693 | 17 |