Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
436 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 10. #16810905 | C4 | semidirect |
| 11. #16810905 | C4 | semidirect |
| 12. #16810830 | C4 | semidirect |
| 13. #16810830 | C4 | semidirect |
| 226. C53 | #9166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284841 | 2 |
| #20283802 | 2 |
| #20274548 | 2 |
| #20273330 | 2 |
| #20272615 | 2 |
| #20272571 | 2 |
| C53×#1503 | 2 |
| #9166 | 53 |