Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
286 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 50 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. #16811532 | C4 | semidirect |
| 9. #16811530 | C4 | semidirect |
| 13. C2×C4×#88322 | C4 | semidirect |
| 14. C53×#382 | C4 | semidirect |
| 139. #382 | #6157 | semidirect |
| 144. C53 | #7502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811532 | 2 |
| C2×#16811530 | 2 |
| #20275524 | 2 |
| #7502 | 53 |