Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
580 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 142 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. #10602687 | C3 | direct (N × H) |
| 20. C22×C3×Dic5 | Q8 | semidirect |
| 56. C22×Dic5 | C3×Q8 | semidirect |
| 134. C3×C5 | #2030 | semidirect |
| 164. C5 | C3×#2030 | semidirect |
| 174. C3 | #10602687 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#543 | 2 |
| C3×#65232 | 2 |
| C3×#64746 | 2 |
| #10602687 | 3 |
| C3×#2030 | 5 |