Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
368 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 3. C3×#65371 | C2 | semidirect |
| 4. C3×#65369 | C2 | semidirect |
| 6. C3×#64685 | C2 | semidirect |
| 7. C3×#64685 | C2 | semidirect |
| 8. #10602040 | C3 | direct (N × H) |
| 31. #65371 | C2×C3 | semidirect |
| 32. #65369 | C2×C3 | semidirect |
| 34. #64685 | C2×C3 | semidirect |
| 35. #64685 | C2×C3 | semidirect |
| 300. C3×C5 | #1664 | semidirect |
| 340. C5 | C3×#1664 | semidirect |
| 354. C3 | #10602040 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66006 | 2 |
| C3×C5×#489 | 2 |
| C3×#65371 | 2 |
| C3×#65369 | 2 |
| C3×#64760 | 2 |
| C3×#64685 | 2 |
| #10602040 | 3 |
| C3×#1664 | 5 |