Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
432 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C4×#10587534 | C2 | semidirect |
| 3. #14544340 | C2 | semidirect |
| 4. #14543681 | C2 | semidirect |
| 15. #11762940 | C4 | semidirect |
| 16. #11762888 | C4 | semidirect |
| 17. #11762886 | C4 | semidirect |
| 24. C17×#446 | C4 | semidirect |
| 139. #3622 | #104 | semidirect |
| 166. #446 | #595 | semidirect |
| 226. C17 | #8668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544657 | 2 |
| C4×#10587534 | 2 |
| #14544340 | 2 |
| #14543681 | 2 |
| #14537749 | 2 |
| #8668 | 17 |