Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
338 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 1. C2×D3×AGL(1,𝔽9) | C2 | semidirect |
| 3. C4⋊(C3⋊AGL(1,𝔽9)) | C2 | semidirect |
| 4. C3×C4×AGL(1,𝔽9) | C2 | semidirect |
| 5. (C2×D3)⋊AGL(1,𝔽9) | C2 | semidirect |
| 20. C4×AGL(1,𝔽9) | D3 | semidirect |
| 29. C3×AGL(1,𝔽9) | D4 | semidirect |
| 30. C4⋊(C3⋊(C3⋊D3)) | C8 | semidirect |
| 32. C32×D12 | C8 | semidirect |
| 33. #6291 | C8 | semidirect |
| 45. C2×C3⋊(C3⋊D3) | C2×C8 | semidirect |
| 47. C2×C32×D3 | C2×C8 | semidirect |
| 54. C33×C4 | C2×C8 | semidirect |
| 55. C3×C3⋊Dic3 | C2×C8 | semidirect |
| 70. AGL(1,𝔽9) | D12 | direct (N × H) |
| 113. C32×C4 | D3×C8 | semidirect |
| 114. C3⋊Dic3 | D3×C8 | semidirect |
| 121. C33 | C8×D4 | semidirect |
| 134. D12 | AGL(1,𝔽9) | direct (N × H) |
| 172. C2×D3 | C2×AGL(1,𝔽9) | semidirect |
| 179. C3×C4 | C2×AGL(1,𝔽9) | semidirect |
| 184. C32 | C8×D12 | semidirect |
| 220. C4 | D3×AGL(1,𝔽9) | semidirect |
| 223. C3 | D4×AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×AGL(1,𝔽9) | 2 |
| D12×#157 | 2 |
| C4⋊(C3⋊AGL(1,𝔽9)) | 2 |
| C3×C4×AGL(1,𝔽9) | 2 |
| (C2×D3)⋊AGL(1,𝔽9) | 2 |
| D4×AGL(1,𝔽9) | 3 |
| C8×D12 | 9 |