Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
536 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 536 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. #14539435 | C2 | semidirect |
| 2. #14537682 | C2 | semidirect |
| 3. #14531000 | C2 | semidirect |
| 4. #14530957 | C2 | semidirect |
| 5. #14530861 | C2 | semidirect |
| 6. #14530860 | C2 | semidirect |
| 7. #14530731 | C2 | semidirect |
| 8. #14530681 | C2 | semidirect |
| 9. #14530679 | C2 | semidirect |
| 10. #14530599 | C2 | semidirect |
| 11. C17×#2231 | C2 | semidirect |
| 17. #11763186 | C22 | semidirect |
| 26. #11762920 | C22 | semidirect |
| 31. #11762631 | C22 | semidirect |
| 32. #11762630 | C22 | semidirect |
| 33. #11762623 | C22 | semidirect |
| 34. #11762621 | C22 | semidirect |
| 37. #11762586 | C22 | semidirect |
| 38. C17×#499 | C22 | semidirect |
| 40. C17×#365 | C22 | semidirect |
| 41. C17×#364 | C22 | semidirect |
| 194. #2231 | D17 | semidirect |
| 223. #499 | C2×D17 | semidirect |
| 240. #365 | C2×D17 | semidirect |
| 242. #364 | C2×D17 | semidirect |
| 304. C17 | #33692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539435 | 2 |
| #14537682 | 2 |
| #14531000 | 2 |
| #14530957 | 2 |
| #14530861 | 2 |
| #14530860 | 2 |
| #14530731 | 2 |
| #14530681 | 2 |
| #14530679 | 2 |
| #14530599 | 2 |
| C17×#2231 | 2 |
| #33692 | 17 |