Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 12. C2×#13133208 | C4 | semidirect |
| 14. #16810521 | C4 | semidirect |
| 19. #16810488 | C4 | semidirect |
| 22. C53×#389 | C4 | semidirect |
| 200. #389 | #6157 | semidirect |
| 212. C53 | #9886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133274 | 2 |
| #20289891 | 2 |
| #20289588 | 2 |
| #20283024 | 2 |
| #9886 | 53 |