Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
200 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 45 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. C9×#131⋊C3 | C2 | semidirect |
| 3. C9×GU(2,𝔽3) | C2 | semidirect |
| 7. C9×GL(2,𝔽3) | C4 | semidirect |
| 8. C9×#226 | C4 | semidirect |
| 15. C9×#131 | D3 | semidirect |
| 25. #5405 | C9 | direct (N × H) |
| 53. #131⋊C3 | C2×C9 | semidirect |
| 54. GU(2,𝔽3) | C2×C9 | semidirect |
| 85. GL(2,𝔽3) | C4×C9 | semidirect |
| 86. #226 | C4×C9 | semidirect |
| 111. #131 | D3×C9 | semidirect |
| 167. C9 | #5405 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#985 | 2 |
| C9×#131⋊C3 | 2 |
| C9×GU(2,𝔽3) | 2 |
| C3×#5405 | 3 |
| C9×#444 | 3 |
| C9×ΓL(1,𝔽25) | 4 |