Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 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 |
|---|---|---|
| 3. #20275693 | C2 | semidirect |
| 5. #20272605 | C2 | semidirect |
| 6. #20272547 | C2 | semidirect |
| 7. C53×#1485 | C2 | semidirect |
| 10. #16810905 | C4 | semidirect |
| 11. #16810900 | C4 | semidirect |
| 12. #16810830 | C4 | semidirect |
| 13. #16810825 | C4 | semidirect |
| 205. #1485 | D53 | semidirect |
| 238. C53 | #8971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284780 | 2 |
| #20283836 | 2 |
| #20275693 | 2 |
| C4×#13133143 | 2 |
| #20272605 | 2 |
| #20272547 | 2 |
| C53×#1485 | 2 |
| #8971 | 53 |