Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21447578 | C2 | semidirect |
| 5. #21443932 | C2 | semidirect |
| 6. #21443914 | C2 | semidirect |
| 7. C61×#1833 | C2 | semidirect |
| 12. #16839885 | C4 | semidirect |
| 140. #1833 | D61 | semidirect |
| 164. C61 | #12830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454737 | 2 |
| #21447578 | 2 |
| #21447554 | 2 |
| C2×#16839568 | 2 |
| #21443932 | 2 |
| #21443914 | 2 |
| C61×#1833 | 2 |
| #12830 | 61 |