Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
392 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 392 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. #20289925 | C2 | semidirect |
| 5. #20289608 | C2 | semidirect |
| 6. #20289602 | C2 | semidirect |
| 14. #16811480 | C4 | semidirect |
| 15. #16811479 | C4 | semidirect |
| 21. Q8×#88322 | C4 | semidirect |
| 22. #16810702 | C4 | semidirect |
| 25. #16810688 | C4 | semidirect |
| 30. C53×#446 | C4 | semidirect |
| 178. #446 | #6157 | semidirect |
| 200. C53 | #8248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290433 | 2 |
| #20290167 | 2 |
| #20290088 | 2 |
| #20289925 | 2 |
| #20289608 | 2 |
| #20289602 | 2 |
| #20283689 | 2 |
| #8248 | 53 |