Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
634 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 195 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 |
|---|---|---|
| 2. C2×C9×C4⋊Dic3 | C2 | semidirect |
| 3. C3×C9×#95 | C2 | semidirect |
| 17. C9×#95 | D3 | semidirect |
| 27. #4677 | C9 | direct (N × H) |
| 50. C2×C4⋊Dic3 | C2×C9 | semidirect |
| 52. C3×#95 | C2×C9 | semidirect |
| 111. #95 | D3×C9 | semidirect |
| 112. C3×C9 | #399 | semidirect |
| 170. C9 | #4677 | direct (N × H) |
| 199. C3 | C9×#399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×(C2×D3)⋊C4 | 2 |
| C2×C9×C4⋊Dic3 | 2 |
| C3×C9×#95 | 2 |
| C3×#4677 | 3 |
| C9×#399 | 3 |