Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
314 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 80 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. C3×C4×PSU(3,𝔽2) | C2 | semidirect |
| 4. C3×C4×AGL(1,𝔽9) | C2 | semidirect |
| 5. C3×AGL(1,𝔽9)⋊C4 | C2 | semidirect |
| 6. C3×PSU(3,𝔽2)⋊C4 | C2 | semidirect |
| 8. C4×AΓL(1,𝔽9) | C3 | direct (N × H) |
| 13. C3×AΓL(1,𝔽9) | C4 | direct (N × H) |
| 22. C4×PSU(3,𝔽2) | C2×C3 | semidirect |
| 24. C4×AGL(1,𝔽9) | C2×C3 | semidirect |
| 25. AGL(1,𝔽9)⋊C4 | C2×C3 | semidirect |
| 26. PSU(3,𝔽2)⋊C4 | C2×C3 | semidirect |
| 34. C3×PSU(3,𝔽2) | C2×C4 | semidirect |
| 38. C3×AGL(1,𝔽9) | C2×C4 | semidirect |
| 48. AΓL(1,𝔽9) | C3×C4 | direct (N × H) |
| 66. C33×C4 | SD16 | semidirect |
| 67. C3×C3⋊Dic3 | SD16 | semidirect |
| 83. PSU(3,𝔽2) | C2×C3×C4 | semidirect |
| 87. AGL(1,𝔽9) | C2×C3×C4 | semidirect |
| 135. C32×C4 | C3×SD16 | semidirect |
| 136. C3⋊Dic3 | C3×SD16 | semidirect |
| 148. C33 | C4×SD16 | semidirect |
| 216. C3×C4 | AΓL(1,𝔽9) | direct (N × H) |
| 221. C32 | C3×C4×SD16 | semidirect |
| 259. C4 | C3×AΓL(1,𝔽9) | direct (N × H) |
| 262. C3 | C4×AΓL(1,𝔽9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×AΓL(1,𝔽9) | 2 |
| C3×C4×PSU(3,𝔽2) | 2 |
| C3×C4×GO+(4,𝔽2) | 2 |
| C3×C4×AGL(1,𝔽9) | 2 |
| C3×AGL(1,𝔽9)⋊C4 | 2 |
| C3×PSU(3,𝔽2)⋊C4 | 2 |
| C3×GO+(4,𝔽2)⋊C4 | 2 |
| C4×AΓL(1,𝔽9) | 3 |
| C3×C4×SD16 | 9 |