Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
698 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 110 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. #14544641 | C2 | semidirect |
| 3. #14543960 | C2 | semidirect |
| 4. #14543657 | C2 | semidirect |
| 15. C2×#10587579 | C4 | semidirect |
| 17. #11762711 | C4 | semidirect |
| 21. C4⋊C4×Dic17 | C4 | semidirect |
| 23. C17×#389 | C4 | semidirect |
| 236. #389 | #595 | semidirect |
| 296. C17 | #8573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544641 | 2 |
| C2×#11763661 | 2 |
| #14543960 | 2 |
| #14543657 | 2 |
| #14531292 | 2 |
| #8573 | 17 |