Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
149 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 149 conjugacy classes of subgroups — too many to draw. Only its 40 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. C4×PSU(3,𝔽2) | C2 | semidirect |
| 4. C4×AGL(1,𝔽9) | C2 | semidirect |
| 5. AGL(1,𝔽9)⋊C4 | C2 | semidirect |
| 6. PSU(3,𝔽2)⋊C4 | C2 | semidirect |
| 12. AΓL(1,𝔽9) | C4 | direct (N × H) |
| 26. PSU(3,𝔽2) | C2×C4 | semidirect |
| 30. AGL(1,𝔽9) | C2×C4 | semidirect |
| 46. C32×C4 | SD16 | semidirect |
| 47. C3⋊Dic3 | SD16 | semidirect |
| 88. C32 | C4×SD16 | semidirect |
| 120. 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×AΓL(1,𝔽9) | 2 |
| C4×PSU(3,𝔽2) | 2 |
| C4×GO+(4,𝔽2) | 2 |
| C4×AGL(1,𝔽9) | 2 |
| AGL(1,𝔽9)⋊C4 | 2 |
| PSU(3,𝔽2)⋊C4 | 2 |
| GO+(4,𝔽2)⋊C4 | 2 |
| C4×SD16 | 9 |