Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
422 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 80 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. D61⋊(C22⋊C16) | C2 | semidirect |
| 2. #21461695 | C2 | semidirect |
| 3. #21460807 | C2 | semidirect |
| 4. #21460805 | C2 | semidirect |
| 14. #16840000 | C4 | semidirect |
| 16. #16839995 | C4 | semidirect |
| 20. #16839800 | C4 | semidirect |
| 22. C2×#135×C61 | C4 | semidirect |
| 177. C2×#135 | #6923 | semidirect |
| 194. C61 | #11885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊(C22⋊C16) | 2 |
| #21461695 | 2 |
| #21460807 | 2 |
| #21460805 | 2 |
| #21455396 | 2 |
| #11885 | 61 |