Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
212 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 75 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. C3×C9×M32 | C2 | semidirect |
| 3. C9×#819 | C2 | semidirect |
| 17. C9×M32 | D3 | semidirect |
| 27. #4516 | C9 | direct (N × H) |
| 50. C3×M32 | C2×C9 | semidirect |
| 53. #819 | C2×C9 | semidirect |
| 103. M32 | D3×C9 | semidirect |
| 105. C3×C9 | #361 | semidirect |
| 152. C9 | #4516 | direct (N × H) |
| 174. C3 | C9×#361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D24 | 2 |
| C3×C9×M32 | 2 |
| C9×#819 | 2 |
| C3×#4516 | 3 |
| C9×#361 | 3 |