Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 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. C4⋊(C3⋊AGL(1,𝔽9)) | C2 | semidirect |
| 3. C3×C4⋊AGL(1,𝔽9) | C2 | semidirect |
| 5. Dic3×AGL(1,𝔽9) | C2 | semidirect |
| 19. C4⋊AGL(1,𝔽9) | D3 | semidirect |
| 31. C4×C3⋊(C3⋊D3) | C8 | semidirect |
| 33. C32×C4×D3 | C8 | semidirect |
| 34. #6289 | C8 | semidirect |
| 36. D3×C3⋊Dic3 | C8 | semidirect |
| 138. C33 | #431 | semidirect |
| 160. C4×D3 | AGL(1,𝔽9) | semidirect |
| 212. C32 | #4833 | semidirect |
| 257. C3 | #10596484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D3×#157 | 2 |
| C4⋊(C3⋊AGL(1,𝔽9)) | 2 |
| C3×C4⋊AGL(1,𝔽9) | 2 |
| (C2×D3)⋊AGL(1,𝔽9) | 2 |
| Dic3×AGL(1,𝔽9) | 2 |
| #10596484 | 3 |
| #4833 | 9 |