Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
474 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 80 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. #21462657 | C2 | semidirect |
| 2. #21461582 | C2 | semidirect |
| 3. #21461275 | C2 | semidirect |
| 4. #21461210 | C2 | semidirect |
| 5. #21460706 | C2 | semidirect |
| 6. #21460685 | C2 | semidirect |
| 25. #16840044 | C4 | semidirect |
| 26. #16839963 | C4 | semidirect |
| 27. #16839957 | C4 | semidirect |
| 32. C61×#474 | C4 | semidirect |
| 214. #474 | #6923 | semidirect |
| 235. C61 | #9161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462657 | 2 |
| #21461582 | 2 |
| #21461275 | 2 |
| #21461210 | 2 |
| #21460706 | 2 |
| #21460685 | 2 |
| #21455972 | 2 |
| #9161 | 61 |