Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
776 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 107 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. #14528772 | C2 | semidirect |
| 2. #14527105 | C2 | semidirect |
| 3. #14526781 | C2 | semidirect |
| 8. #11762576 | C22 | semidirect |
| 10. #11762533 | C22 | semidirect |
| 11. C23×D4×C17 | C4 | semidirect |
| 15. C17×#394 | C4 | semidirect |
| 18. C17×#380 | C4 | semidirect |
| 197. C23×D4 | Dic17 | semidirect |
| 203. #394 | Dic17 | semidirect |
| 207. #380 | Dic17 | semidirect |
| 253. C17 | #11873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14528772 | 2 |
| #14527105 | 2 |
| #14526781 | 2 |
| C17×#2408 | 2 |
| #11873 | 17 |