Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×C22⋊#11719908 | C2 | semidirect |
| 3. #20272726 | C2 | semidirect |
| 4. #20272723 | C2 | semidirect |
| 5. C53×#1807 | C2 | semidirect |
| 6. C2×#13133239 | C4 | semidirect |
| 9. #16810864 | C4 | semidirect |
| 11. #16810859 | C4 | semidirect |
| 15. #16810661 | C4 | semidirect |
| 167. #1807 | D53 | semidirect |
| 194. C53 | #11885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284296 | 2 |
| C2×C22⋊#11719908 | 2 |
| #20272726 | 2 |
| #20272723 | 2 |
| C53×#1807 | 2 |
| #11885 | 53 |