Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
558 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×#16839564 | C2 | semidirect |
| 3. #21445848 | C2 | semidirect |
| 4. #21443911 | C2 | semidirect |
| 5. C22×M32×C61 | C2 | semidirect |
| 9. #16839998 | C4 | semidirect |
| 48. C2×C16×C61 | D4 | semidirect |
| 139. C22×M32 | D61 | semidirect |
| 165. C61 | #13061 | semidirect |
| 188. C2×C16 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839998 | 2 |
| C2×#16839564 | 2 |
| #21445848 | 2 |
| #21443911 | 2 |
| C22×M32×C61 | 2 |
| #13061 | 61 |