Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
456 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 86 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. #14544664 | C2 | semidirect |
| 2. #14544660 | C2 | semidirect |
| 4. #14543684 | C2 | semidirect |
| 14. C2×#10587593 | C4 | semidirect |
| 21. #11762775 | C4 | semidirect |
| 23. #11762765 | C4 | semidirect |
| 24. C17×#424 | C4 | semidirect |
| 192. #424 | #595 | semidirect |
| 248. C17 | #8626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544664 | 2 |
| #14544660 | 2 |
| #14544201 | 2 |
| #14543684 | 2 |
| #14537477 | 2 |
| #8626 | 17 |