Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
384 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 384 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. C4×#10587534 | C2 | semidirect |
| 2. #14544347 | C2 | semidirect |
| 4. #14543636 | C2 | semidirect |
| 15. #11762940 | C4 | semidirect |
| 16. #11762886 | C4 | semidirect |
| 19. C8×D68 | C4 | semidirect |
| 24. C8×Q8×C17 | C4 | semidirect |
| 158. C8×Q8 | #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 |
| #14544347 | 2 |
| #14544188 | 2 |
| #14543636 | 2 |
| #14537761 | 2 |
| #8697 | 17 |