Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
260 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 6. #10600089 | C3 | direct (N × H) |
| 33. C3×Dic20 | Q8 | semidirect |
| 82. Dic20 | C3×Q8 | semidirect |
| 167. C3×C5 | #2227 | semidirect |
| 194. C5 | C3×#2227 | semidirect |
| 203. C3 | #10600089 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Dic20 | 2 |
| C3×#64971 | 2 |
| C3×C5×C4⋊C16 | 2 |
| C3×#64724 | 2 |
| C3×#64723 | 2 |
| #10600089 | 3 |
| C3×#2227 | 5 |