Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. C2×#16839578 | C2 | semidirect |
| 5. #21443922 | C2 | semidirect |
| 6. #21443905 | C2 | semidirect |
| 7. C61×#1979 | C2 | semidirect |
| 12. C2×#14519723 | C4 | semidirect |
| 13. C2×#14519720 | C4 | semidirect |
| 165. #1979 | D61 | semidirect |
| 192. C61 | #13035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840203 | 2 |
| #21454737 | 2 |
| C2×#16839578 | 2 |
| #21447546 | 2 |
| #21443922 | 2 |
| #21443905 | 2 |
| C61×#1979 | 2 |
| #13035 | 61 |