Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 5. C2×#13133288 | C4 | semidirect |
| 6. C2×#13133287 | C4 | semidirect |
| 13. #16810405 | C4 | semidirect |
| 15. C53×#349 | C4 | semidirect |
| 147. #349 | #6157 | semidirect |
| 151. C53 | #7256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290596 | 2 |
| #20290387 | 2 |
| #349×D53 | 2 |
| #7256 | 53 |