Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
580 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 580 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 |
|---|---|---|
| 3. #20272737 | C2 | semidirect |
| 5. C23×Dic106 | C4 | semidirect |
| 8. #16810543 | C4 | semidirect |
| 14. #16810483 | C4 | semidirect |
| 193. C53 | #11898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20278080 | 2 |
| #20274703 | 2 |
| #20272737 | 2 |
| C53×#1460 | 2 |
| #11898 | 53 |