Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 90 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. D61⋊#504 | C2 | semidirect |
| 2. #21462140 | C2 | semidirect |
| 3. C2×#16840676 | C2 | semidirect |
| 4. #21461706 | C2 | semidirect |
| 5. #21460898 | C2 | semidirect |
| 6. #21460882 | C2 | semidirect |
| 25. #16840038 | C4 | semidirect |
| 26. #16840037 | C4 | semidirect |
| 27. #16840029 | C4 | semidirect |
| 32. C61×#472 | C4 | semidirect |
| 239. #472 | #6923 | semidirect |
| 251. C61 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#504 | 2 |
| #21462140 | 2 |
| C2×#16840676 | 2 |
| #21461706 | 2 |
| #21460898 | 2 |
| #21460882 | 2 |
| #21455537 | 2 |
| #13071 | 61 |