Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 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 |
|---|---|---|
| 3. #20273227 | C2 | semidirect |
| 5. #20272576 | C2 | semidirect |
| 6. #20272543 | C2 | semidirect |
| 7. C53×#1497 | C2 | semidirect |
| 9. #16811026 | C4 | semidirect |
| 10. #16811019 | C4 | semidirect |
| 11. #16810971 | C4 | semidirect |
| 12. #16810971 | C4 | semidirect |
| 168. #1497 | D53 | semidirect |
| 197. C53 | #9279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285851 | 2 |
| #20283790 | 2 |
| #20273227 | 2 |
| #20273224 | 2 |
| #20272576 | 2 |
| #20272543 | 2 |
| C53×#1497 | 2 |
| #9279 | 53 |