Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21445867 | C2 | semidirect |
| 4. #21445863 | C2 | semidirect |
| 5. #21443949 | C2 | semidirect |
| 6. #21443947 | C2 | semidirect |
| 9. C22×#11758194 | C4 | semidirect |
| 16. #16839789 | C4 | semidirect |
| 20. #16839726 | C4 | semidirect |
| 21. #16839718 | C4 | semidirect |
| 237. C61 | #12806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454523 | 2 |
| #21447460 | 2 |
| #21445867 | 2 |
| #21445863 | 2 |
| #21443949 | 2 |
| #21443947 | 2 |
| C61×#2120 | 2 |
| #12806 | 61 |