Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
646 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 646 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. #20283179 | C2 | semidirect |
| 3. #20276386 | C2 | semidirect |
| 4. #20276366 | C2 | semidirect |
| 5. #20272845 | C2 | semidirect |
| 6. #20272835 | C2 | semidirect |
| 7. C53×#1796 | C2 | semidirect |
| 8. C2×#13133242 | C4 | semidirect |
| 9. C22×#11719924 | C4 | semidirect |
| 16. #16810632 | C4 | semidirect |
| 17. #16810619 | C4 | semidirect |
| 245. #1796 | D53 | semidirect |
| 278. C53 | #13103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284001 | 2 |
| #20283179 | 2 |
| #20276386 | 2 |
| #20276366 | 2 |
| #20272845 | 2 |
| #20272835 | 2 |
| C53×#1796 | 2 |
| #13103 | 53 |