Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 7. #16810420 | C4 | semidirect |
| 9. #16810418 | C4 | semidirect |
| 13. C2×#97×C53 | C4 | semidirect |
| 14. C53×#384 | C4 | semidirect |
| 138. C2×#97 | Dic53 | semidirect |
| 139. #384 | Dic53 | semidirect |
| 144. C53 | #7508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810420 | 2 |
| C2×#16810418 | 2 |
| C53×#1959 | 2 |
| #7508 | 53 |