Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
314 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21447592 | C2 | semidirect |
| 5. #21446567 | C2 | semidirect |
| 6. #21443931 | C2 | semidirect |
| 7. C61×#2150 | C2 | semidirect |
| 138. #2150 | D61 | semidirect |
| 164. C61 | #13466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447592 | 2 |
| #21447556 | 2 |
| #21447548 | 2 |
| #21446707 | 2 |
| #21446567 | 2 |
| #21443931 | 2 |
| C61×#2150 | 2 |
| #13466 | 61 |