Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 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 |
|---|---|---|
| 2. #20283373 | C2 | semidirect |
| 5. #20272591 | C2 | semidirect |
| 6. #20272563 | C2 | semidirect |
| 7. C53×#1826 | C2 | semidirect |
| 16. C2×#13133150 | C4 | semidirect |
| 17. C2×#13133148 | C4 | semidirect |
| 19. C2×#13133137 | C4 | semidirect |
| 20. C2×#13133137 | C4 | semidirect |
| 218. #1826 | D53 | semidirect |
| 256. C53 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810947 | 2 |
| #20283373 | 2 |
| #20273230 | 2 |
| #20273076 | 2 |
| #20272591 | 2 |
| #20272563 | 2 |
| C53×#1826 | 2 |
| #9242 | 53 |