Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
434 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 19. #11763728 | C4 | semidirect |
| 26. #11762626 | C4 | semidirect |
| 27. #11762625 | C4 | semidirect |
| 28. #11762624 | C4 | semidirect |
| 29. C17×#362 | C4 | semidirect |
| 171. #595 | #362 | direct (N × H) |
| 196. #362 | #595 | direct (N × H) |
| 247. C17 | C4×#362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×#595 | 2 |
| D17⋊#362 | 2 |
| M32×#595 | 2 |
| #108×#595 | 2 |
| #14543860 | 2 |
| #14543859 | 2 |
| D17×#362 | 2 |
| C4×#362 | 17 |