Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
392 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 88 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. #21460895 | C2 | semidirect |
| 4. #21460885 | C2 | semidirect |
| 15. #16839811 | C4 | semidirect |
| 18. #16839809 | C4 | semidirect |
| 21. C61×#430 | C4 | semidirect |
| 172. #430 | #6923 | semidirect |
| 181. C61 | #12875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#349 | 2 |
| #21461697 | 2 |
| #21460895 | 2 |
| #21460885 | 2 |
| #430×D61 | 2 |
| #12875 | 61 |