Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #101×Dic53 | C2 | semidirect |
| 4. #20272841 | C2 | semidirect |
| 16. #16810420 | C4 | semidirect |
| 20. C53×#355 | C4 | semidirect |
| 35. #13133136 | C2×C4 | semidirect |
| 50. #101×C53 | C2×C4 | semidirect |
| 172. #355 | Dic53 | semidirect |
| 174. C53 | #12632 | semidirect |
| 199. #101 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277428 | 2 |
| C2×#16810420 | 2 |
| #101×Dic53 | 2 |
| #20272841 | 2 |
| C2×C53×#355 | 2 |
| #12632 | 53 |