Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
544 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 14. #16810488 | C4 | semidirect |
| 15. #16810488 | C4 | semidirect |
| 19. C4×C4⋊Dic53 | C4 | semidirect |
| 22. C4×C4⋊C4×C53 | C4 | semidirect |
| 200. C4×C4⋊C4 | #6157 | semidirect |
| 208. C53 | #8714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290607 | 2 |
| #20289891 | 2 |
| #20289588 | 2 |
| #20277111 | 2 |
| #8714 | 53 |