Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
468 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 468 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. #20274815 | C2 | semidirect |
| 4. #20274784 | C2 | semidirect |
| 5. #20272603 | C2 | semidirect |
| 6. #20272563 | C2 | semidirect |
| 10. #16810956 | C4 | semidirect |
| 11. #16810951 | C4 | semidirect |
| 13. #16810939 | C4 | semidirect |
| 14. #16810934 | C4 | semidirect |
| 264. C53 | #9038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284624 | 2 |
| #20283763 | 2 |
| #20274815 | 2 |
| #20274784 | 2 |
| #20272603 | 2 |
| #20272563 | 2 |
| C53×#1501 | 2 |
| #9038 | 53 |