Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
504 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 132 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×#65729 | C2 | semidirect |
| 5. C3×#64901 | C2 | semidirect |
| 6. #10603928 | C3 | direct (N × H) |
| 24. #65729 | C2×C3 | semidirect |
| 26. #64901 | C2×C3 | semidirect |
| 244. C3×C5 | #1858 | semidirect |
| 280. C5 | C3×#1858 | semidirect |
| 290. C3 | #10603928 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66256 | 2 |
| C3×#65776 | 2 |
| C3×#65729 | 2 |
| C3×#65034 | 2 |
| C3×#64901 | 2 |
| #10603928 | 3 |
| C3×#1858 | 5 |