Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
172 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 68 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. #10598618 | C3 | direct (N × H) |
| 129. C3×C5 | #1365 | semidirect |
| 154. C5 | C3×#1365 | semidirect |
| 163. C3 | #10598618 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65163 | 2 |
| C3×#64888 | 2 |
| C3×#64884 | 2 |
| #10598618 | 3 |
| C3×#1365 | 5 |