Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
756 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. C2×#16810469 | C2 | semidirect |
| 2. #20274783 | C2 | semidirect |
| 4. #20272593 | C2 | semidirect |
| 16. C53×#390 | C4 | semidirect |
| 17. C53×#389 | C4 | semidirect |
| 179. #390 | Dic53 | semidirect |
| 180. #389 | Dic53 | semidirect |
| 189. C53 | #9149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810469 | 2 |
| #20274783 | 2 |
| C2×#16810357 | 2 |
| #20272593 | 2 |
| C53×#2854 | 2 |
| #9149 | 53 |