Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
312 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #21447416 | C2 | semidirect |
| 5. #21443933 | C2 | semidirect |
| 6. #21443916 | C2 | semidirect |
| 7. C61×#1953 | C2 | semidirect |
| 14. #16839577 | C4 | semidirect |
| 15. #16839574 | C4 | semidirect |
| 140. #1953 | D61 | semidirect |
| 165. C61 | #13146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447566 | 2 |
| C2×#16839568 | 2 |
| #21447416 | 2 |
| #21446717 | 2 |
| #21443933 | 2 |
| #21443916 | 2 |
| C61×#1953 | 2 |
| #13146 | 61 |