Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
920 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. #21456372 | C2 | semidirect |
| 4. #21451767 | C2 | semidirect |
| 6. #21446662 | C2 | semidirect |
| 7. #21446035 | C2 | semidirect |
| 9. C61×#1995 | C2 | semidirect |
| 190. #1995 | D61 | semidirect |
| 225. C61 | #25691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21459706 | 2 |
| #21456372 | 2 |
| #21455642 | 2 |
| #21451767 | 2 |
| #21447039 | 2 |
| #21446662 | 2 |
| #21446035 | 2 |
| #21445630 | 2 |
| C61×#1995 | 2 |
| #25691 | 61 |