Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
614 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 134 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. #16810672 | C4 | semidirect |
| 16. #16810671 | C4 | semidirect |
| 19. C53×#430 | C4 | semidirect |
| 173. #430 | #6157 | semidirect |
| 179. C53 | #11375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290408 | 2 |
| D53⋊#338 | 2 |
| #20290377 | 2 |
| #430×D53 | 2 |
| #11375 | 53 |