Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
242 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 1. C9×2−1+4⋊C3 | C2 | semidirect |
| 2. C9×#986 | C2 | semidirect |
| 3. C9×GU(2,𝔽3) | C2 | semidirect |
| 13. C9×2−1+4 | D3 | semidirect |
| 25. #5431 | C9 | direct (N × H) |
| 52. 2−1+4⋊C3 | C2×C9 | semidirect |
| 53. #986 | C2×C9 | semidirect |
| 57. GU(2,𝔽3) | C2×C9 | semidirect |
| 119. 2−1+4 | D3×C9 | semidirect |
| 186. C9 | #5431 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×2−1+4⋊C3 | 2 |
| C9×#986 | 2 |
| C9×GU(2,𝔽3) | 2 |
| C3×#5431 | 3 |
| C9×#454 | 3 |
| C9×#213 | 4 |