Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. C2×D3×Dic20 | C2 | semidirect |
| 3. C2×#90944 | C2 | semidirect |
| 4. C2×#90941 | C2 | semidirect |
| 5. #11746313 | C2 | semidirect |
| 6. C3×#64712 | C2 | semidirect |
| 7. (C2×D3)⋊#672 | C2 | semidirect |
| 31. #64712 | D3 | semidirect |
| 44. Dic60 | D4 | semidirect |
| 52. C3×Dic20 | D4 | semidirect |
| 136. Dic20 | D12 | semidirect |
| 152. C2×C5×D3 | SD32 | semidirect |
| 282. C3×C5 | #2185 | semidirect |
| 289. C2×D3 | #3959 | semidirect |
| 327. C5 | #69223 | semidirect |
| 341. C3 | #10601870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Dic20 | 2 |
| C5×#4883 | 2 |
| C2×#90944 | 2 |
| C2×#90941 | 2 |
| #11746313 | 2 |
| C3×#64712 | 2 |
| (C2×D3)⋊#672 | 2 |
| #10601870 | 3 |
| #69223 | 5 |