Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
478 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 91 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. #14537868 | C2 | semidirect |
| 3. C4×#10587495 | C2 | semidirect |
| 6. #14526648 | C2 | semidirect |
| 7. C17×#1288 | C2 | semidirect |
| 186. #1288 | D17 | semidirect |
| 289. C17 | #9188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537868 | 2 |
| #14534647 | 2 |
| C4×#10587495 | 2 |
| #14527383 | 2 |
| #14527381 | 2 |
| #14526648 | 2 |
| C17×#1288 | 2 |
| #9188 | 17 |