Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
394 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 3. C4×C3⋊AGL(1,𝔽9) | C2 | semidirect |
| 4. C3×C4×AGL(1,𝔽9) | C2 | semidirect |
| 5. Dic3×AGL(1,𝔽9) | C2 | semidirect |
| 11. D3×AGL(1,𝔽9) | C4 | direct (N × H) |
| 21. C4×AGL(1,𝔽9) | D3 | direct (N × H) |
| 27. D3×#157 | C8 | semidirect |
| 29. C3⋊AGL(1,𝔽9) | C2×C4 | semidirect |
| 30. C3×AGL(1,𝔽9) | C2×C4 | semidirect |
| 31. C4×C3⋊(C3⋊D3) | C8 | semidirect |
| 33. C32×C4×D3 | C8 | semidirect |
| 34. #6289 | C8 | semidirect |
| 36. D3×C3⋊Dic3 | C8 | semidirect |
| 55. C3⋊#157 | C2×C8 | semidirect |
| 56. C3×#157 | C2×C8 | semidirect |
| 58. C33×C4 | C2×C8 | semidirect |
| 59. C3⋊(C3⋊Dic3) | C2×C8 | semidirect |
| 60. C3×C3⋊Dic3 | C2×C8 | semidirect |
| 61. C32×Dic3 | C2×C8 | semidirect |
| 76. AGL(1,𝔽9) | C4×D3 | direct (N × H) |
| 92. C3⋊(C3⋊D3) | C4×C8 | semidirect |
| 95. C32×D3 | C4×C8 | semidirect |
| 120. #157 | D3×C8 | semidirect |
| 125. C32×C4 | D3×C8 | semidirect |
| 129. C3⋊Dic3 | D3×C8 | semidirect |
| 137. C33 | C2×C4×C8 | semidirect |
| 158. C4×D3 | AGL(1,𝔽9) | direct (N × H) |
| 200. C3×C4 | C2×AGL(1,𝔽9) | semidirect |
| 207. Dic3 | C2×AGL(1,𝔽9) | semidirect |
| 210. C32 | C4×D3×C8 | semidirect |
| 237. D3 | C4×AGL(1,𝔽9) | direct (N × H) |
| 250. C4 | D3×AGL(1,𝔽9) | direct (N × H) |
| 253. C3 | C2×C4×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 |
| C4×D3×#157 | 2 |
| C4×C3⋊AGL(1,𝔽9) | 2 |
| C3×C4×AGL(1,𝔽9) | 2 |
| Dic3×AGL(1,𝔽9) | 2 |
| C2×C4×AGL(1,𝔽9) | 3 |
| C4×D3×C8 | 9 |