Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
640 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20276406 | C2 | semidirect |
| 3. #20276366 | C2 | semidirect |
| 4. #20274690 | C2 | semidirect |
| 5. #20272845 | C2 | semidirect |
| 6. #20272837 | C2 | semidirect |
| 7. C53×#2889 | C2 | semidirect |
| 8. C2×#13133242 | C4 | semidirect |
| 9. C22×#11719924 | C4 | semidirect |
| 17. #16810632 | C4 | semidirect |
| 18. #16810619 | C4 | semidirect |
| 240. #2889 | D53 | semidirect |
| 276. C53 | #13098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284001 | 2 |
| #20276406 | 2 |
| #20276366 | 2 |
| #20274690 | 2 |
| #20272845 | 2 |
| #20272837 | 2 |
| C53×#2889 | 2 |
| #13098 | 53 |