Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 12. #16811663 | C4 | semidirect |
| 13. #16811663 | C4 | semidirect |
| 19. #16811536 | C4 | semidirect |
| 26. #16810440 | C4 | semidirect |
| 27. #16810439 | C4 | semidirect |
| 28. #16810438 | C4 | semidirect |
| 29. C53×#362 | C4 | semidirect |
| 192. #362 | #6157 | semidirect |
| 197. C53 | #12648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811663 | 2 |
| #20291025 | 2 |
| #20290930 | 2 |
| #20290524 | 2 |
| #20289787 | 2 |
| #20289781 | 2 |
| #362×D53 | 2 |
| #12648 | 53 |