Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21458807 | C2 | semidirect |
| 2. #21448087 | C2 | semidirect |
| 4. #21447881 | C2 | semidirect |
| 6. #21447868 | C2 | semidirect |
| 7. #21447727 | C2 | semidirect |
| 8. #21447682 | C2 | semidirect |
| 9. C4×Q32×C61 | C2 | semidirect |
| 148. C4×Q32 | D61 | semidirect |
| 178. C61 | #33969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458807 | 2 |
| #21448087 | 2 |
| #21448080 | 2 |
| #21447881 | 2 |
| #21447877 | 2 |
| #21447868 | 2 |
| #21447727 | 2 |
| #21447682 | 2 |
| C4×Q32×C61 | 2 |
| #33969 | 61 |