Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #20273330 | C2 | semidirect |
| 5. #20272615 | C2 | semidirect |
| 6. #20272596 | C2 | semidirect |
| 7. C53×#1518 | C2 | semidirect |
| 9. #16811029 | C4 | semidirect |
| 10. #16811015 | C4 | semidirect |
| 11. #16810991 | C4 | semidirect |
| 12. #16810985 | C4 | semidirect |
| 196. #1518 | D53 | semidirect |
| 233. C53 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285418 | 2 |
| #20283704 | 2 |
| #20273330 | 2 |
| #20273251 | 2 |
| #20272615 | 2 |
| #20272596 | 2 |
| C53×#1518 | 2 |
| #9431 | 53 |