Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
346 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
| 21. C4⋊AGL(1,𝔽9) | D3 | direct (N × H) |
| 32. C4×C3⋊(C3⋊D3) | C8 | semidirect |
| 34. C32×C4×D3 | C8 | semidirect |
| 35. #6289 | C8 | semidirect |
| 37. D3×C3⋊Dic3 | C8 | semidirect |
| 60. C33×C4 | C2×C8 | semidirect |
| 61. C3⋊(C3⋊Dic3) | C2×C8 | semidirect |
| 62. C3×C3⋊Dic3 | C2×C8 | semidirect |
| 63. C32×Dic3 | C2×C8 | semidirect |
| 95. C3⋊(C3⋊D3) | C4⋊C8 | semidirect |
| 98. C32×D3 | C4⋊C8 | semidirect |
| 129. C32×C4 | D3×C8 | semidirect |
| 133. C3⋊Dic3 | D3×C8 | semidirect |
| 141. C33 | C2×C4⋊C8 | semidirect |
| 163. C4×D3 | AGL(1,𝔽9) | semidirect |
| 206. C3×C4 | C2×AGL(1,𝔽9) | semidirect |
| 213. Dic3 | C2×AGL(1,𝔽9) | semidirect |
| 216. C32 | D3×C4⋊C8 | semidirect |
| 244. D3 | C4⋊AGL(1,𝔽9) | direct (N × H) |
| 258. C4 | D3×AGL(1,𝔽9) | semidirect |
| 261. 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 |
| D3×C4⋊C8 | 9 |