Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
590 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 144 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×C32×PSU(3,𝔽2) | C2 | semidirect |
| 3. C2×C32×AGL(1,𝔽9) | C2 | semidirect |
| 4. C32×AΓL(1,𝔽9) | C2 | direct (N × H) |
| 5. C2×C3×AΓL(1,𝔽9) | C3 | direct (N × H) |
| 10. C32×PSU(3,𝔽2) | C22 | semidirect |
| 13. C32×AGL(1,𝔽9) | C22 | semidirect |
| 14. C2×C3×PSU(3,𝔽2) | C2×C3 | semidirect |
| 16. C2×C3×AGL(1,𝔽9) | C2×C3 | semidirect |
| 17. C3×AΓL(1,𝔽9) | C2×C3 | direct (N × H) |
| 25. C2×AΓL(1,𝔽9) | C32 | direct (N × H) |
| 32. C3×PSU(3,𝔽2) | C22×C3 | semidirect |
| 35. C3×AGL(1,𝔽9) | C22×C3 | semidirect |
| 36. C2×C34 | SD16 | semidirect |
| 37. C32×C3⋊D3 | SD16 | semidirect |
| 40. C2×PSU(3,𝔽2) | C2×C32 | semidirect |
| 42. C2×AGL(1,𝔽9) | C2×C32 | semidirect |
| 43. AΓL(1,𝔽9) | C2×C32 | direct (N × H) |
| 62. C34 | C2×SD16 | semidirect |
| 69. PSU(3,𝔽2) | C22×C32 | semidirect |
| 72. AGL(1,𝔽9) | C22×C32 | semidirect |
| 83. C2×C33 | C3×SD16 | semidirect |
| 84. C3×C3⋊D3 | C3×SD16 | semidirect |
| 119. C33 | C2×C3×SD16 | semidirect |
| 138. C2×C32 | C32×SD16 | semidirect |
| 139. C2×C32 | AΓL(1,𝔽9) | direct (N × H) |
| 140. C3⋊D3 | C32×SD16 | semidirect |
| 168. C32 | C2×C32×SD16 | semidirect |
| 169. C32 | C2×AΓL(1,𝔽9) | direct (N × H) |
| 185. C2×C3 | C3×AΓL(1,𝔽9) | direct (N × H) |
| 198. C3 | C2×C3×AΓL(1,𝔽9) | direct (N × H) |
| 202. C2 | C32×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×C32×PSU(3,𝔽2) | 2 |
| C2×C32×GO+(4,𝔽2) | 2 |
| C2×C32×AGL(1,𝔽9) | 2 |
| C32×AΓL(1,𝔽9) | 2 |
| C2×C3×AΓL(1,𝔽9) | 3 |
| C2×C32×SD16 | 9 |