Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
770 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 175 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. #14539530 | C2 | semidirect |
| 3. #14539325 | C2 | semidirect |
| 5. #14528458 | C2 | semidirect |
| 6. #14528453 | C2 | semidirect |
| 7. #14528418 | C2 | semidirect |
| 8. #14528403 | C2 | semidirect |
| 9. #14528402 | C2 | semidirect |
| 10. #14527086 | C2 | semidirect |
| 11. C17×#1705 | C2 | semidirect |
| 157. C8×C17 | #137 | semidirect |
| 169. #1705 | D17 | semidirect |
| 265. C17 | #19746 | semidirect |
| 336. C8 | #10587601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539530 | 2 |
| #14539500 | 2 |
| #14539325 | 2 |
| #14539238 | 2 |
| #14528458 | 2 |
| #14528453 | 2 |
| #14528418 | 2 |
| #14528403 | 2 |
| #14528402 | 2 |
| #14527086 | 2 |
| C17×#1705 | 2 |
| #19746 | 17 |