Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
786 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 95 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. C4×#10587505 | C2 | semidirect |
| 2. #14527125 | 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 |
| 189. C23×D4 | Dic17 | semidirect |
| 195. #394 | Dic17 | semidirect |
| 198. #380 | Dic17 | semidirect |
| 243. C17 | #11772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587505 | 2 |
| #14527125 | 2 |
| #14526781 | 2 |
| C17×#2408 | 2 |
| #11772 | 17 |