Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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. #14539443 | C2 | semidirect |
| 2. #14531003 | C2 | semidirect |
| 3. #14530960 | C2 | semidirect |
| 4. #14530865 | C2 | semidirect |
| 6. #14530675 | C2 | semidirect |
| 7. #14530600 | C2 | semidirect |
| 11. #11763211 | C22 | semidirect |
| 12. #11763189 | C22 | semidirect |
| 16. #11762917 | C22 | semidirect |
| 18. #11762633 | C22 | semidirect |
| 19. #11762630 | C22 | semidirect |
| 20. #11762624 | C22 | semidirect |
| 23. #11762587 | C22 | semidirect |
| 231. C17 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539443 | 2 |
| #14531003 | 2 |
| #14530960 | 2 |
| #14530865 | 2 |
| #14530735 | 2 |
| #14530675 | 2 |
| #14530600 | 2 |
| C17×#2955 | 2 |
| #33693 | 17 |