Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
466 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 82 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. #21461505 | C2 | semidirect |
| 3. #21460808 | C2 | semidirect |
| 4. #21460805 | C2 | semidirect |
| 12. C2×#14519796 | C4 | semidirect |
| 16. #16840003 | C4 | semidirect |
| 20. #16839799 | C4 | semidirect |
| 22. C61×#466 | C4 | semidirect |
| 187. #466 | #6923 | semidirect |
| 196. C61 | #11703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊(C22⋊C16) | 2 |
| #21461505 | 2 |
| #21460808 | 2 |
| #21460805 | 2 |
| #21455398 | 2 |
| #11703 | 61 |