Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. #20273339 | C2 | semidirect |
| 3. #20272865 | C2 | semidirect |
| 4. C2×C53×#354 | C2 | semidirect |
| 5. C2×#13133265 | C4 | semidirect |
| 9. #16810795 | C4 | semidirect |
| 13. C2×#13133136 | C4 | semidirect |
| 15. #16810363 | C22 | semidirect |
| 19. C53×#354 | C22 | semidirect |
| 23. #13133265 | C2×C4 | semidirect |
| 38. #13133136 | C2×C4 | semidirect |
| 171. C2×#354 | D53 | semidirect |
| 193. #354 | C2×D53 | semidirect |
| 196. C53 | #13569 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810795 | 2 |
| #20273339 | 2 |
| #20272865 | 2 |
| C2×C53×#354 | 2 |
| #13569 | 53 |