Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
488 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 59 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⋊(C3⋊GU(2,𝔽3)) | C2 | semidirect |
| 3. C32×GU(2,𝔽3) | C2 | semidirect |
| 7. C3⋊D3×SL(2,𝔽3) | C4 | semidirect |
| 8. C3⋊(C3⋊(#41⋊C3)) | C4 | semidirect |
| 16. C3×GU(2,𝔽3) | D3 | semidirect |
| 56. GU(2,𝔽3) | C3⋊D3 | semidirect |
| 188. C32 | #5423 | semidirect |
| 224. C3 | #10593228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#41⋊C3 | 2 |
| C3⋊(C3⋊GU(2,𝔽3)) | 2 |
| C32×GU(2,𝔽3) | 2 |
| #10593228 | 3 |
| #10592520 | 3 |
| #88787 | 4 |