Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
676 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #20283760 | C2 | semidirect |
| 3. #20274660 | C2 | semidirect |
| 4. #20274626 | C2 | semidirect |
| 5. #20273204 | C2 | semidirect |
| 6. #20272603 | C2 | semidirect |
| 7. C53×#1282 | C2 | semidirect |
| 12. #16810781 | C4 | semidirect |
| 13. #16810776 | C4 | semidirect |
| 15. #16810764 | C4 | semidirect |
| 16. #16810759 | C4 | semidirect |
| 287. #1282 | D53 | semidirect |
| 324. C53 | #9037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283937 | 2 |
| #20283760 | 2 |
| #20274660 | 2 |
| #20274626 | 2 |
| #20273204 | 2 |
| #20272603 | 2 |
| C53×#1282 | 2 |
| #9037 | 53 |