Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
518 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 11. #16810345 | C4 | semidirect |
| 12. #16810344 | C4 | semidirect |
| 15. C82×C53 | C4 | semidirect |
| 86. C82 | Dic53 | semidirect |
| 87. C53 | #7844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274460 | 2 |
| C4×#13133127 | 2 |
| C2×#16810345 | 2 |
| C2×#16810344 | 2 |
| C2×C82×C53 | 2 |
| #7844 | 53 |