Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
672 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21447493 | C2 | semidirect |
| 4. #21447474 | C2 | semidirect |
| 5. #21443949 | C2 | semidirect |
| 6. #21443939 | C2 | semidirect |
| 8. C2×#14519807 | C4 | semidirect |
| 9. C22×#11758200 | C4 | semidirect |
| 16. #16839767 | C4 | semidirect |
| 17. #16839758 | C4 | semidirect |
| 31. C22×Dic122 | C2×C4 | semidirect |
| 38. C2×#11758194 | C2×C4 | semidirect |
| 39. C22×#92418 | C2×C4 | semidirect |
| 50. #14519736 | C2×C4 | semidirect |
| 282. C61 | #13100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455096 | 2 |
| #21454280 | 2 |
| #21447493 | 2 |
| #21447474 | 2 |
| #21443949 | 2 |
| #21443939 | 2 |
| C61×#1795 | 2 |
| #13100 | 61 |