Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
380 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 90 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×#6762 | C2 | semidirect |
| 3. C2×C3×#704 | C2 | semidirect |
| 4. (C2×D3)⋊#170 | C2 | semidirect |
| 14. C2×C3⋊#170 | C22 | semidirect |
| 16. C2×C3×#170 | C22 | semidirect |
| 20. C2×#704 | D3 | semidirect |
| 51. C2×#170 | C2×D3 | semidirect |
| 59. C2×C5×D3 | M16 | semidirect |
| 135. C3×C5 | #407 | semidirect |
| 142. C2×D3 | #704 | semidirect |
| 170. C5 | #5126 | semidirect |
| 182. C3 | #65798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×Dic5 | 2 |
| C2×#6762 | 2 |
| C2×C3×#704 | 2 |
| (C2×D3)⋊#170 | 2 |
| #65798 | 3 |
| #5126 | 5 |