Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
334 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 59 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. #16810416 | C4 | semidirect |
| 9. #16810367 | C4 | semidirect |
| 11. C53×#518 | C4 | semidirect |
| 13. C2×#100×C53 | C4 | semidirect |
| 139. #518 | Dic53 | semidirect |
| 142. C2×#100 | Dic53 | semidirect |
| 149. C53 | #7493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810416 | 2 |
| #20273429 | 2 |
| C53×#1887 | 2 |
| #7493 | 53 |