Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
512 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 143 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. #21456469 | C2 | semidirect |
| 2. #21447977 | C2 | semidirect |
| 3. #21447922 | C2 | semidirect |
| 4. #21447905 | C2 | semidirect |
| 5. #21447855 | C2 | semidirect |
| 6. C61×#2151 | C2 | semidirect |
| 105. #2151 | D61 | semidirect |
| 128. C61 | #33825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456469 | 2 |
| #21447977 | 2 |
| #21447922 | 2 |
| #21447905 | 2 |
| #21447855 | 2 |
| C61×#2151 | 2 |
| #33825 | 61 |