Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
444 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 16. #16810666 | C4 | semidirect |
| 17. #16810666 | C4 | semidirect |
| 19. #16810631 | C4 | semidirect |
| 20. #16810631 | C4 | semidirect |
| 244. C53 | #9346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284663 | 2 |
| #20283373 | 2 |
| #20273286 | 2 |
| #20273078 | 2 |
| #20272621 | 2 |
| #20272603 | 2 |
| C53×#1825 | 2 |
| #9346 | 53 |