Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
478 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 92 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. D61⋊#361 | C2 | semidirect |
| 3. C2×#16840674 | C2 | semidirect |
| 4. #21461708 | C2 | semidirect |
| 5. #21460895 | C2 | semidirect |
| 6. #21460878 | C2 | semidirect |
| 25. #16840033 | C4 | semidirect |
| 26. #16840032 | C4 | semidirect |
| 29. #16840029 | C4 | semidirect |
| 32. C61×#472 | C4 | semidirect |
| 252. #472 | #6923 | semidirect |
| 262. C61 | #13073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#504 | 2 |
| D61⋊#361 | 2 |
| C2×#16840674 | 2 |
| #21461708 | 2 |
| #21460895 | 2 |
| #21460878 | 2 |
| #472×D61 | 2 |
| #13073 | 61 |