Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21458831 | C2 | semidirect |
| 2. #21448082 | C2 | semidirect |
| 3. #21448080 | C2 | semidirect |
| 4. #21447880 | C2 | semidirect |
| 5. #21447874 | C2 | semidirect |
| 6. #21447853 | C2 | semidirect |
| 7. #21447727 | C2 | semidirect |
| 8. #21447682 | C2 | semidirect |
| 9. C4×D16×C61 | C2 | semidirect |
| 153. C4×D16 | D61 | semidirect |
| 184. C61 | #33970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458831 | 2 |
| #21448082 | 2 |
| #21448080 | 2 |
| #21447880 | 2 |
| #21447874 | 2 |
| #21447853 | 2 |
| #21447727 | 2 |
| #21447682 | 2 |
| C4×D16×C61 | 2 |
| #33970 | 61 |