Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
188 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 188 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. #10598030 | C3 | direct (N × H) |
| 6. C3×#4016 | C4 | semidirect |
| 11. C3×#3935 | C4 | semidirect |
| 29. #4016 | C3×C4 | semidirect |
| 34. #3935 | C3×C4 | semidirect |
| 137. C3×C5 | #1412 | semidirect |
| 167. C5 | C3×#1412 | semidirect |
| 178. C3 | #10598030 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65360 | 2 |
| C3×C5×#353 | 2 |
| C3×#64765 | 2 |
| #10598030 | 3 |
| C3×#1412 | 5 |