Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
416 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C3×#65011 | C2 | semidirect |
| 4. C3×#64948 | C2 | semidirect |
| 6. C3×#64689 | C2 | semidirect |
| 7. C3×#64672 | C2 | semidirect |
| 8. #10599091 | C3 | direct (N × H) |
| 31. #65011 | C2×C3 | semidirect |
| 32. #64948 | C2×C3 | semidirect |
| 34. #64689 | C2×C3 | semidirect |
| 35. #64672 | C2×C3 | semidirect |
| 331. C3×C5 | #1615 | semidirect |
| 386. C5 | C3×#1615 | semidirect |
| 404. C3 | #10599091 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65936 | 2 |
| C3×#65323 | 2 |
| C3×#65011 | 2 |
| C3×#64948 | 2 |
| C3×C5×#327 | 2 |
| C3×#64689 | 2 |
| C3×#64672 | 2 |
| #10599091 | 3 |
| C3×#1615 | 5 |