Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
392 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20273483 | C2 | semidirect |
| 4. #20272607 | C2 | semidirect |
| 13. #16810363 | C4 | semidirect |
| 14. #16810363 | C4 | semidirect |
| 15. #16810363 | C4 | semidirect |
| 159. C53 | #8918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275548 | 2 |
| #20273483 | 2 |
| #20273307 | 2 |
| #20272607 | 2 |
| C53×#2980 | 2 |
| #8918 | 53 |