Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1326 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 1326 conjugacy classes of subgroups — too many to draw. Only its 352 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 |
|---|---|---|
| 7. #16811569 | C4 | semidirect |
| 8. #16811568 | C4 | semidirect |
| 12. #16810491 | C4 | semidirect |
| 13. #16810490 | C4 | semidirect |
| 15. C53×#383 | C4 | semidirect |
| 52. C42×C53 | C42 | semidirect |
| 53. C4×Dic53 | C42 | semidirect |
| 106. #383 | #6157 | semidirect |
| 110. C53 | #13830 | semidirect |
| 148. C42 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811569 | 2 |
| C2×#16811568 | 2 |
| #20289895 | 2 |
| #383×D53 | 2 |
| #13830 | 53 |