Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 15. #16810754 | C4 | semidirect |
| 16. #16810753 | C4 | semidirect |
| 19. #16810750 | C4 | semidirect |
| 24. C53×#446 | C4 | semidirect |
| 170. #446 | #6157 | semidirect |
| 183. C53 | #8657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290636 | 2 |
| #20290584 | 2 |
| D53⋊#334 | 2 |
| #20289594 | 2 |
| #446×D53 | 2 |
| #8657 | 53 |