Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
932 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#16840677 | C2 | semidirect |
| 2. C2×#16840676 | C2 | semidirect |
| 3. D61⋊(C22⋊C16) | C2 | semidirect |
| 4. #21461699 | C2 | semidirect |
| 6. C2×D61⋊C16 | C22 | semidirect |
| 7. C2×#14519848 | C22 | semidirect |
| 221. C2×D61 | #359 | semidirect |
| 264. C61 | #12734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840677 | 2 |
| C2×#16840676 | 2 |
| D61⋊(C22⋊C16) | 2 |
| #21461699 | 2 |
| C2×#135×D61 | 2 |
| #12734 | 61 |