Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
512 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 127 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. #21456462 | C2 | semidirect |
| 2. #21447978 | C2 | semidirect |
| 3. #21447975 | C2 | semidirect |
| 4. #21447922 | C2 | semidirect |
| 5. #21447903 | C2 | semidirect |
| 6. #21447853 | C2 | semidirect |
| 7. #21447852 | C2 | semidirect |
| 8. #21447579 | C2 | semidirect |
| 9. C61×#2218 | C2 | semidirect |
| 149. #2218 | D61 | semidirect |
| 184. C61 | #33825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456462 | 2 |
| #21447978 | 2 |
| #21447975 | 2 |
| #21447922 | 2 |
| #21447903 | 2 |
| #21447853 | 2 |
| #21447852 | 2 |
| #21447579 | 2 |
| C61×#2218 | 2 |
| #33825 | 61 |