Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
186 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21447701 | C2 | semidirect |
| 3. #21444023 | C2 | semidirect |
| 4. #21444004 | C2 | semidirect |
| 5. C4×C32×C61 | C2 | semidirect |
| 8. Dic976 | C4 | semidirect |
| 9. #16839601 | C4 | semidirect |
| 10. D1952 | C4 | semidirect |
| 64. C4×C32 | D61 | semidirect |
| 78. C61 | #13655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448128 | 2 |
| #21447701 | 2 |
| #21444023 | 2 |
| #21444004 | 2 |
| C4×C32×C61 | 2 |
| #13655 | 61 |