Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 96 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×C3⋊#672 | C2 | semidirect |
| 3. C2×C3×#672 | C2 | semidirect |
| 4. #90935 | C2 | direct (N × H) |
| 11. C3⋊#672 | C22 | semidirect |
| 12. C3×#672 | C22 | semidirect |
| 17. C2×#672 | D3 | semidirect |
| 36. #672 | C2×D3 | semidirect |
| 63. C2×C3×C5 | M32 | semidirect |
| 87. C3×C5 | C2×M32 | semidirect |
| 95. C2×C5 | #798 | semidirect |
| 105. C2×C3 | #3944 | semidirect |
| 108. C5 | C2×#798 | semidirect |
| 115. C3 | C2×#3944 | semidirect |
| 117. C2 | #90935 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×C8 | 2 |
| C2×C3⋊#672 | 2 |
| C2×C3×#672 | 2 |
| #90935 | 2 |
| C2×#3944 | 3 |
| C2×#798 | 5 |