Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
572 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 222 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 |
|---|---|---|
| 7. C9⋊#564 | C3 | direct (N × H) |
| 141. C3×C9 | #564 | semidirect |
| 190. C9 | C3×#564 | semidirect |
| 209. C3 | C9⋊#564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#125 | 2 |
| C3×#63452 | 2 |
| C3×#63451 | 2 |
| C3×#63432 | 2 |
| C3×C3⋊#564 | 3 |
| C9⋊#564 | 3 |