Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. #20273214 | C2 | semidirect |
| 5. #20272614 | C2 | semidirect |
| 6. #20272570 | C2 | semidirect |
| 7. C53×#1531 | C2 | semidirect |
| 10. #16810900 | C4 | semidirect |
| 11. #16810900 | C4 | semidirect |
| 12. #16810825 | C4 | semidirect |
| 13. #16810825 | C4 | semidirect |
| 207. #1531 | D53 | semidirect |
| 243. C53 | #9165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284810 | 2 |
| #20283752 | 2 |
| #20274541 | 2 |
| #20273214 | 2 |
| #20272614 | 2 |
| #20272570 | 2 |
| C53×#1531 | 2 |
| #9165 | 53 |