Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
826 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
|---|---|---|
| 18. #16811003 | C4 | semidirect |
| 19. #16811002 | C4 | semidirect |
| 20. #16811001 | C4 | semidirect |
| 22. C53×#494 | C4 | semidirect |
| 125. #494 | #6157 | semidirect |
| 135. C53 | #22277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291206 | 2 |
| #20290846 | 2 |
| #20290709 | 2 |
| #20290637 | 2 |
| #20290433 | 2 |
| #494×D53 | 2 |
| #22277 | 53 |