Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 20. #16811026 | C4 | semidirect |
| 21. #16811002 | C4 | semidirect |
| 22. #16810974 | C4 | semidirect |
| 26. C53×#487 | C4 | semidirect |
| 166. #487 | #6157 | semidirect |
| 180. C53 | #9853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290900 | 2 |
| #20290428 | 2 |
| #20290270 | 2 |
| #20290065 | 2 |
| #20290064 | 2 |
| #20285300 | 2 |
| #9853 | 53 |