Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
147 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 147 conjugacy classes of subgroups — too many to draw. Only its 32 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. PSU(3,𝔽2)⋊C4 | C2 | semidirect |
| 39. C32×C4 | SD16 | semidirect |
| 40. C3⋊Dic3 | SD16 | semidirect |
| 77. C32 | #461 | semidirect |
| 106. C4 | AΓL(1,𝔽9) | semidirect |
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 |
| PSU(3,𝔽2)⋊C4 | 2 |
| #461 | 9 |