Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #20273227 | C2 | semidirect |
| 5. #20272609 | C2 | semidirect |
| 6. #20272587 | C2 | semidirect |
| 7. C53×#1526 | C2 | semidirect |
| 10. #16810915 | C4 | semidirect |
| 11. #16810910 | C4 | semidirect |
| 12. #16810830 | C4 | semidirect |
| 13. #16810825 | C4 | semidirect |
| 193. #1526 | D53 | semidirect |
| 227. C53 | #9160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284871 | 2 |
| #20283733 | 2 |
| #20274528 | 2 |
| #20273227 | 2 |
| #20272609 | 2 |
| #20272587 | 2 |
| C53×#1526 | 2 |
| #9160 | 53 |