Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1088 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 151 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×C4×C22⋊Dic53 | C2 | semidirect |
| 2. #20274625 | C2 | semidirect |
| 3. C2×#16810357 | C2 | semidirect |
| 4. #20272593 | C2 | semidirect |
| 14. C2×#121×C53 | C4 | semidirect |
| 19. C53×#380 | C4 | semidirect |
| 31. #13133124 | D4 | semidirect |
| 212. C2×#121 | Dic53 | semidirect |
| 221. #380 | Dic53 | semidirect |
| 226. C53 | #9150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊Dic53 | 2 |
| #20274625 | 2 |
| C2×#16810357 | 2 |
| #20272593 | 2 |
| C53×#2847 | 2 |
| #9150 | 53 |