Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
334 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 9. #16811027 | C4 | semidirect |
| 10. #16811001 | C4 | semidirect |
| 14. Q16×Dic53 | C4 | semidirect |
| 15. #16810717 | C4 | semidirect |
| 183. C53 | #11857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285296 | 2 |
| #20276511 | 2 |
| #20274841 | 2 |
| #20272728 | 2 |
| #20272727 | 2 |
| #20272726 | 2 |
| C53×#1348 | 2 |
| #11857 | 53 |