Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
730 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 159 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. #14539936 | C2 | semidirect |
| 3. #14539527 | C2 | semidirect |
| 5. #14528460 | C2 | semidirect |
| 6. #14528456 | C2 | semidirect |
| 7. #14528440 | C2 | semidirect |
| 8. #14528415 | C2 | semidirect |
| 9. #14528385 | C2 | semidirect |
| 10. #14527078 | C2 | semidirect |
| 11. C17×#1713 | C2 | semidirect |
| 166. #1713 | D17 | semidirect |
| 263. C17 | #19731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539936 | 2 |
| #14539923 | 2 |
| #14539527 | 2 |
| #14539242 | 2 |
| #14528460 | 2 |
| #14528456 | 2 |
| #14528440 | 2 |
| #14528415 | 2 |
| #14528385 | 2 |
| #14527078 | 2 |
| C17×#1713 | 2 |
| #19731 | 17 |