Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
284 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 106 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×#65005 | C2 | semidirect |
| 5. C3×#64716 | C2 | semidirect |
| 6. C3×#64714 | C2 | semidirect |
| 7. C3×#64686 | C2 | semidirect |
| 8. #10601721 | C3 | direct (N × H) |
| 16. C3×#3961 | C4 | semidirect |
| 17. C3×#3959 | C4 | semidirect |
| 25. #65005 | C2×C3 | semidirect |
| 27. #64716 | C2×C3 | semidirect |
| 28. #64714 | C2×C3 | semidirect |
| 29. #64686 | C2×C3 | semidirect |
| 62. #3961 | C3×C4 | semidirect |
| 63. #3959 | C3×C4 | semidirect |
| 217. C3×C5 | #2180 | semidirect |
| 246. C5 | C3×#2180 | semidirect |
| 255. C3 | #10601721 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#444 | 2 |
| C3×#65484 | 2 |
| C3×#65005 | 2 |
| C3×#64786 | 2 |
| C3×#64716 | 2 |
| C3×#64714 | 2 |
| C3×#64686 | 2 |
| #10601721 | 3 |
| C3×#2180 | 5 |