Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1090 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 9. C53×#543 | C4 | semidirect |
| 13. C23×Dic53 | Q8 | semidirect |
| 21. C2×C22⋊Dic53 | Q8 | semidirect |
| 132. #543 | Dic53 | semidirect |
| 139. C53 | #11394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810389 | 2 |
| C2×C53×#543 | 2 |
| #11394 | 53 |