Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
662 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 19. #16810388 | C4 | semidirect |
| 20. #16810387 | C4 | semidirect |
| 21. C53×#341 | C4 | semidirect |
| 178. #341 | #6157 | semidirect |
| 180. C53 | #11332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811638 | 2 |
| C22×#13133287 | 2 |
| C2×#16811506 | 2 |
| #20290380 | 2 |
| #341×D53 | 2 |
| #11332 | 53 |