Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
400 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 100 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. #20290433 | C2 | semidirect |
| 4. C8×#11719936 | C2 | semidirect |
| 5. #20289608 | C2 | semidirect |
| 6. #20289602 | C2 | semidirect |
| 14. #16811480 | C4 | semidirect |
| 15. #16811478 | C4 | semidirect |
| 21. #16810753 | C4 | semidirect |
| 22. #16810747 | C4 | semidirect |
| 24. D4×#88322 | C4 | semidirect |
| 30. C53×#436 | C4 | semidirect |
| 180. #436 | #6157 | semidirect |
| 200. C53 | #8250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290433 | 2 |
| #20290165 | 2 |
| #20290086 | 2 |
| C8×#11719936 | 2 |
| #20289608 | 2 |
| #20289602 | 2 |
| #20283693 | 2 |
| #8250 | 53 |