Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
334 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 3. #20272890 | C2 | semidirect |
| 11. C53×#533 | C4 | semidirect |
| 15. C53×#488 | C4 | semidirect |
| 19. C4×M16×C53 | C4 | semidirect |
| 30. #125×C53 | C2×C4 | semidirect |
| 46. C4×C8×C53 | C2×C4 | semidirect |
| 141. #533 | Dic53 | semidirect |
| 145. #488 | Dic53 | semidirect |
| 151. C4×M16 | Dic53 | semidirect |
| 156. C53 | #13603 | semidirect |
| 162. #125 | C2×Dic53 | semidirect |
| 183. 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×#16810420 | 2 |
| C2×#16810418 | 2 |
| #20272890 | 2 |
| C53×#3140 | 2 |
| #13603 | 53 |