Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
328 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 8. #10598889 | C3 | direct (N × H) |
| 209. C3×C5 | #1718 | semidirect |
| 238. C5 | C3×#1718 | semidirect |
| 247. C3 | #10598889 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64971 | 2 |
| C3×#64970 | 2 |
| C3×#64969 | 2 |
| C3×C5×#322 | 2 |
| #10598889 | 3 |
| C3×#1718 | 5 |