Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
434 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 100 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. #14544721 | C2 | semidirect |
| 2. #14544334 | C2 | semidirect |
| 4. #14543639 | C2 | semidirect |
| 16. #11762887 | C4 | semidirect |
| 17. #11762886 | C4 | semidirect |
| 19. C8×D68 | C4 | semidirect |
| 24. C8×D4×C17 | C4 | semidirect |
| 188. C8×D4 | #595 | semidirect |
| 246. C17 | #8676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544721 | 2 |
| #14544334 | 2 |
| #14544214 | 2 |
| #14543639 | 2 |
| #14537491 | 2 |
| #8676 | 17 |