Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
450 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 2. C4×D61⋊C16 | C2 | semidirect |
| 3. C4×#14519848 | C2 | semidirect |
| 4. #21460880 | C2 | semidirect |
| 9. #16840677 | C4 | direct (N × H) |
| 26. D61⋊C16 | C2×C4 | semidirect |
| 29. #14519848 | C2×C4 | semidirect |
| 142. C4×C61 | #359 | semidirect |
| 147. Dic61 | #359 | semidirect |
| 177. C61 | C4×#359 | semidirect |
| 299. C4 | #16840677 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840677 | 2 |
| C4×D61⋊C16 | 2 |
| C4×#14519848 | 2 |
| #21460880 | 2 |
| C4×#14519800 | 2 |
| C4×#359 | 61 |