Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
270 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 270 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. #16810345 | C4 | semidirect |
| 17. #16810344 | C4 | semidirect |
| 145. C53 | #8794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274886 | 2 |
| #20274845 | 2 |
| #20273008 | 2 |
| #20272575 | 2 |
| #20272574 | 2 |
| #20272573 | 2 |
| C53×#1286 | 2 |
| #8794 | 53 |