Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 79 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×#16810416 | C2 | semidirect |
| 2. #20272880 | C2 | semidirect |
| 3. #20272878 | C2 | semidirect |
| 9. C53×#532 | C4 | semidirect |
| 12. C53×#493 | C4 | semidirect |
| 14. C53×#492 | C4 | semidirect |
| 16. C4×M16×C53 | C4 | semidirect |
| 30. C4⋊Q8×C53 | C2×C4 | semidirect |
| 33. #127×C53 | C2×C4 | semidirect |
| 41. C4×C8×C53 | C2×C4 | semidirect |
| 42. C4×C8×C53 | C2×C4 | semidirect |
| 136. #532 | Dic53 | semidirect |
| 139. #493 | Dic53 | semidirect |
| 141. #492 | Dic53 | semidirect |
| 144. C4×M16 | Dic53 | semidirect |
| 147. C53 | #13584 | semidirect |
| 158. C4⋊Q8 | C2×Dic53 | semidirect |
| 161. #127 | C2×Dic53 | semidirect |
| 172. C4×C8 | C2×Dic53 | semidirect |
| 173. C4×C8 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810416 | 2 |
| #20272880 | 2 |
| #20272878 | 2 |
| C53×#3151 | 2 |
| #13584 | 53 |