Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
418 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 90 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. #14544706 | C2 | semidirect |
| 2. #14544332 | C2 | semidirect |
| 4. #14543639 | C2 | semidirect |
| 16. #11762888 | C4 | semidirect |
| 18. D4×#3622 | C4 | semidirect |
| 19. #11762874 | C4 | semidirect |
| 24. C17×#436 | C4 | semidirect |
| 169. #436 | #595 | semidirect |
| 226. C17 | #8680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544706 | 2 |
| #14544332 | 2 |
| #14544214 | 2 |
| #14543639 | 2 |
| #14537493 | 2 |
| #8680 | 17 |