Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
624 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 624 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. #20276409 | C2 | semidirect |
| 3. #20276370 | C2 | semidirect |
| 5. #20272845 | C2 | semidirect |
| 6. #20272837 | C2 | semidirect |
| 8. C2×#13133247 | C4 | semidirect |
| 9. C22×#11719925 | C4 | semidirect |
| 17. #16810632 | C4 | semidirect |
| 18. #16810619 | C4 | semidirect |
| 269. C53 | #13096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284010 | 2 |
| #20276409 | 2 |
| #20276370 | 2 |
| #20274690 | 2 |
| #20272845 | 2 |
| #20272837 | 2 |
| C53×#2889 | 2 |
| #13096 | 53 |