Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
768 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 158 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×#91233 | C2 | semidirect |
| 3. C2×C3×#4002 | C2 | semidirect |
| 4. C2×(C2×D3)⋊#170 | C2 | semidirect |
| 22. C2×#4002 | D3 | semidirect |
| 38. C2×C3×#170 | D4 | semidirect |
| 109. C2×#170 | D12 | semidirect |
| 249. C3×C5 | #1955 | semidirect |
| 297. C5 | #69837 | semidirect |
| 313. C3 | #10604949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic5×D12 | 2 |
| C2×#91233 | 2 |
| C2×C3×#4002 | 2 |
| C2×(C2×D3)⋊#170 | 2 |
| #10604949 | 3 |
| #69837 | 5 |