Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. #20291612 | C2 | semidirect |
| 2. #20290586 | C2 | semidirect |
| 5. #20289605 | C2 | semidirect |
| 6. #20289570 | C2 | semidirect |
| 27. #16810830 | C4 | semidirect |
| 28. #16810824 | C4 | semidirect |
| 29. #16810823 | C4 | semidirect |
| 32. C53×#462 | C4 | semidirect |
| 231. #462 | #6157 | semidirect |
| 250. C53 | #9310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291612 | 2 |
| #20290586 | 2 |
| #20290146 | 2 |
| #20290022 | 2 |
| #20289605 | 2 |
| #20289570 | 2 |
| #20284188 | 2 |
| #9310 | 53 |