Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
424 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 4. C3×#64870 | C2 | semidirect |
| 5. #10604637 | C3 | direct (N × H) |
| 25. #64870 | C2×C3 | semidirect |
| 236. C3×C5 | #1531 | semidirect |
| 273. C5 | C3×#1531 | semidirect |
| 286. C3 | #10604637 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66062 | 2 |
| C3×#65683 | 2 |
| C3×#65676 | 2 |
| C3×#64870 | 2 |
| #10604637 | 3 |
| C3×#1531 | 5 |