Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
306 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
| 4. Dic3⋊AGL(1,𝔽9) | C2 | semidirect |
| 20. C4×AGL(1,𝔽9) | D3 | semidirect |
| 30. C4×C3⋊(C3⋊D3) | C8 | semidirect |
| 32. C32×C4×D3 | C8 | semidirect |
| 33. #6289 | C8 | semidirect |
| 35. D3×C3⋊Dic3 | C8 | semidirect |
| 134. C33 | #431 | semidirect |
| 155. C4×D3 | AGL(1,𝔽9) | semidirect |
| 206. C32 | #4685 | semidirect |
| 249. 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 |
| Dic3⋊AGL(1,𝔽9) | 2 |
| (C2×D3)⋊AGL(1,𝔽9) | 2 |
| #10596484 | 3 |
| #4685 | 9 |