Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1358 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1358 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
| 16. C23×Dic53 | Q8 | semidirect |
| 20. C2×C22⋊Dic53 | Q8 | semidirect |
| 144. #543 | Dic53 | semidirect |
| 150. C53 | #11390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810390 | 2 |
| #20272937 | 2 |
| C2×C53×#543 | 2 |
| #11390 | 53 |