Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 92 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. #91096 | C2 | semidirect |
| 3. C3×#3944 | C2 | semidirect |
| 4. #90935 | C2 | semidirect |
| 5. D3×#672 | C2 | semidirect |
| 14. C3⋊#672 | C22 | semidirect |
| 15. C3×#672 | C22 | semidirect |
| 20. #3944 | D3 | direct (N × H) |
| 46. #672 | C2×D3 | semidirect |
| 84. C5×D3 | M32 | semidirect |
| 113. C3×C5 | C2×M32 | semidirect |
| 140. D3 | #3944 | direct (N × H) |
| 141. C5 | D3×M32 | semidirect |
| 150. C3 | C2×#3944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×C8 | 2 |
| #91096 | 2 |
| C3×#3944 | 2 |
| #90935 | 2 |
| D3×#672 | 2 |
| C2×#3944 | 3 |
| D3×M32 | 5 |