Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 4. C2×#11762586 | C2 | semidirect |
| 5. #14528670 | C2 | semidirect |
| 6. #14526900 | C2 | semidirect |
| 7. C17×#1384 | C2 | semidirect |
| 11. #11762920 | C4 | semidirect |
| 12. #11762915 | C4 | semidirect |
| 18. #11762618 | C4 | semidirect |
| 19. #11762617 | C4 | semidirect |
| 46. C2×C16×C17 | C2×C4 | semidirect |
| 50. C17×#106 | C2×C4 | semidirect |
| 52. #10587490 | C2×C4 | semidirect |
| 56. #10587483 | C2×C4 | semidirect |
| 139. #1384 | D17 | semidirect |
| 200. C2×C16 | C4×D17 | semidirect |
| 206. #106 | C4×D17 | semidirect |
| 213. C17 | #12649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537584 | 2 |
| #14530519 | 2 |
| #14530513 | 2 |
| C2×#11762586 | 2 |
| #14528670 | 2 |
| #14526900 | 2 |
| C17×#1384 | 2 |
| #12649 | 17 |