Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
360 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 41. #10587555 | Q8 | semidirect |
| 42. #10587555 | Q8 | semidirect |
| 229. C17 | #10379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14529727 | 2 |
| #14527334 | 2 |
| #14527295 | 2 |
| #14526677 | 2 |
| #14526648 | 2 |
| #14526640 | 2 |
| C17×#2605 | 2 |
| #10379 | 17 |