Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
468 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 3. #20274786 | C2 | semidirect |
| 5. #20272602 | C2 | semidirect |
| 6. #20272563 | C2 | semidirect |
| 7. C53×#1826 | C2 | semidirect |
| 10. #16810958 | C4 | semidirect |
| 11. #16810953 | C4 | semidirect |
| 13. #16810941 | C4 | semidirect |
| 14. #16810936 | C4 | semidirect |
| 224. #1826 | D53 | semidirect |
| 264. C53 | #9038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284628 | 2 |
| #20283765 | 2 |
| #20274786 | 2 |
| #20273204 | 2 |
| #20272602 | 2 |
| #20272563 | 2 |
| C53×#1826 | 2 |
| #9038 | 53 |