Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
786 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #14527125 | C2 | semidirect |
| 3. #14526780 | C2 | semidirect |
| 4. C4×C17×#99 | C2 | semidirect |
| 5. C23×D68 | C4 | semidirect |
| 9. #11762726 | C4 | semidirect |
| 12. #11762669 | C4 | semidirect |
| 15. #11762533 | C22 | semidirect |
| 19. C17×#342 | C22 | semidirect |
| 155. C4×#99 | D17 | semidirect |
| 201. #342 | C2×D17 | semidirect |
| 243. C17 | #11772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14532140 | 2 |
| #14527125 | 2 |
| #14526780 | 2 |
| C4×C17×#99 | 2 |
| #11772 | 17 |