Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 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. C8×#88322 | C4 | semidirect |
| 143. C53 | #8792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274852 | 2 |
| #20274845 | 2 |
| #20272999 | 2 |
| #20272575 | 2 |
| #20272574 | 2 |
| #20272573 | 2 |
| C53×#1286 | 2 |
| #8792 | 53 |