Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
384 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 88 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. C4×#10587534 | C2 | semidirect |
| 2. #14544345 | C2 | semidirect |
| 4. #14543636 | C2 | semidirect |
| 15. Q8×#3622 | C4 | semidirect |
| 16. #11762888 | C4 | semidirect |
| 19. #11762874 | C4 | semidirect |
| 24. C17×#446 | C4 | semidirect |
| 157. #446 | #595 | semidirect |
| 217. C17 | #8697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587534 | 2 |
| #14544345 | 2 |
| #14544188 | 2 |
| #14543636 | 2 |
| #14537758 | 2 |
| #8697 | 17 |