Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 9. #16811029 | C4 | semidirect |
| 10. #16811029 | C4 | semidirect |
| 210. C53 | #9440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285268 | 2 |
| #20277820 | 2 |
| #20273341 | 2 |
| #20273227 | 2 |
| #20272608 | 2 |
| #20272607 | 2 |
| C53×#1506 | 2 |
| #9440 | 53 |