Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
456 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 131 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. #14528584 | C2 | semidirect |
| 3. #14526907 | C2 | semidirect |
| 4. #14526905 | C2 | semidirect |
| 9. #11762599 | C4 | semidirect |
| 10. #11762596 | C4 | semidirect |
| 13. C22×M16×C17 | C4 | semidirect |
| 17. C17×#424 | C4 | semidirect |
| 19. C17×#407 | C4 | semidirect |
| 20. C17×#405 | C4 | semidirect |
| 144. C22×M16 | Dic17 | semidirect |
| 148. #424 | Dic17 | semidirect |
| 152. #407 | Dic17 | semidirect |
| 154. #405 | Dic17 | semidirect |
| 194. C17 | #12624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14530425 | 2 |
| #14528584 | 2 |
| #14526907 | 2 |
| #14526905 | 2 |
| C17×#2930 | 2 |
| #12624 | 17 |