Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20274864 | C2 | semidirect |
| 3. #20272710 | C2 | semidirect |
| 5. #20272704 | C2 | semidirect |
| 7. C53×#2165 | C2 | semidirect |
| 9. #16811025 | C4 | semidirect |
| 10. #16811007 | C4 | semidirect |
| 15. #16810736 | C4 | semidirect |
| 16. #16810731 | C4 | semidirect |
| 137. #2165 | D53 | semidirect |
| 166. C53 | #11836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285444 | 2 |
| #20274864 | 2 |
| #20272710 | 2 |
| #20272707 | 2 |
| #20272704 | 2 |
| #20272701 | 2 |
| C53×#2165 | 2 |
| #11836 | 53 |