Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
168 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 46 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. #10598034 | C3 | direct (N × H) |
| 6. C3×#4016 | C4 | semidirect |
| 11. C3×C4×#168 | C4 | semidirect |
| 29. #4016 | C3×C4 | semidirect |
| 34. C4×#168 | C3×C4 | semidirect |
| 129. C3×C5 | #1414 | semidirect |
| 154. C5 | C3×#1414 | semidirect |
| 163. C3 | #10598034 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65345 | 2 |
| C3×C5×#354 | 2 |
| C3×#64762 | 2 |
| #10598034 | 3 |
| C3×#1414 | 5 |