Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
356 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 17. #16810369 | C4 | semidirect |
| 18. #16810369 | C4 | semidirect |
| 19. #16810369 | C4 | semidirect |
| 20. #16810369 | C4 | semidirect |
| 178. C53 | #8936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275693 | 2 |
| #20273503 | 2 |
| #20273380 | 2 |
| #20272547 | 2 |
| C53×#2986 | 2 |
| #8936 | 53 |