Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1244 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 323 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 |
|---|---|---|
| 1. #20283847 | C2 | semidirect |
| 2. #20273450 | C2 | semidirect |
| 3. #20273383 | C2 | semidirect |
| 4. #20273377 | C2 | semidirect |
| 8. #16810676 | C22 | semidirect |
| 9. #16810647 | C22 | semidirect |
| 10. #16810372 | C22 | semidirect |
| 11. #16810372 | C22 | semidirect |
| 12. #16810367 | C22 | semidirect |
| 13. #16810367 | C22 | semidirect |
| 137. C53 | #17782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283847 | 2 |
| #20273450 | 2 |
| #20273383 | 2 |
| #20273377 | 2 |
| C53×#3498 | 2 |
| #17782 | 53 |