Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
500 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 68 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. #14544484 | C2 | semidirect |
| 2. #14544038 | C2 | semidirect |
| 3. #14543781 | C2 | semidirect |
| 12. C2×#10587579 | C4 | semidirect |
| 15. #11762726 | C4 | semidirect |
| 21. #11762676 | C4 | semidirect |
| 22. C17×#400 | C4 | semidirect |
| 196. #400 | #595 | semidirect |
| 252. C17 | #11754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544484 | 2 |
| #14544038 | 2 |
| #14543781 | 2 |
| #14543763 | 2 |
| #14534353 | 2 |
| #11754 | 17 |