Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
482 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #20277367 | C2 | semidirect |
| 5. #20273163 | C2 | semidirect |
| 6. #20272572 | C2 | semidirect |
| 7. C53×#1300 | C2 | semidirect |
| 11. #16810919 | C4 | semidirect |
| 12. #16810824 | C4 | semidirect |
| 180. #1300 | D53 | semidirect |
| 209. C53 | #9330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284838 | 2 |
| #20277367 | 2 |
| #20275634 | 2 |
| #20273222 | 2 |
| #20273163 | 2 |
| #20272572 | 2 |
| C53×#1300 | 2 |
| #9330 | 53 |