Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
402 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 106 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. C4×D61⋊C16 | C2 | semidirect |
| 2. #21461369 | C2 | semidirect |
| 3. #21460775 | C2 | semidirect |
| 4. #21460774 | C2 | semidirect |
| 30. #14519800 | C8 | semidirect |
| 170. C61 | #11591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D61⋊C16 | 2 |
| #21461369 | 2 |
| #21460775 | 2 |
| #21460774 | 2 |
| C4×#14519800 | 2 |
| #11591 | 61 |