Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
394 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 4. Dic3×AGL(1,𝔽9) | C2 | direct (N × H) |
| 8. C2×C3⋊AGL(1,𝔽9) | C4 | semidirect |
| 10. C2×C3×AGL(1,𝔽9) | C4 | semidirect |
| 20. C2×C3⋊#157 | C8 | semidirect |
| 26. C3⋊AGL(1,𝔽9) | C2×C4 | semidirect |
| 27. C3×AGL(1,𝔽9) | C2×C4 | semidirect |
| 28. C2×C3⋊(C3⋊Dic3) | C8 | semidirect |
| 29. C2×C32×Dic3 | C8 | semidirect |
| 30. Dic3×C3⋊D3 | C8 | semidirect |
| 37. C2×AGL(1,𝔽9) | Dic3 | direct (N × H) |
| 48. C3⋊#157 | C2×C8 | semidirect |
| 52. C3⋊(C3⋊Dic3) | C2×C8 | semidirect |
| 53. C32×Dic3 | C2×C8 | semidirect |
| 67. AGL(1,𝔽9) | C2×Dic3 | direct (N × H) |
| 78. C2×C33 | C4×C8 | semidirect |
| 80. C3×C3⋊D3 | C4×C8 | semidirect |
| 117. C33 | C2×C4×C8 | semidirect |
| 132. C2×Dic3 | AGL(1,𝔽9) | direct (N × H) |
| 141. C2×C32 | C8×Dic3 | semidirect |
| 143. C3⋊D3 | C8×Dic3 | semidirect |
| 177. Dic3 | C2×AGL(1,𝔽9) | direct (N × H) |
| 180. C32 | C2×C8×Dic3 | semidirect |
| 201. C2×C3 | C4×AGL(1,𝔽9) | semidirect |
| 219. C3 | C2×C4×AGL(1,𝔽9) | semidirect |
| 223. C2 | Dic3×AGL(1,𝔽9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊AGL(1,𝔽9) | 2 |
| C22×C3×AGL(1,𝔽9) | 2 |
| C2×Dic3×#157 | 2 |
| Dic3×AGL(1,𝔽9) | 2 |
| C2×C4×AGL(1,𝔽9) | 3 |
| C2×C8×Dic3 | 9 |