Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
185 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 185 conjugacy classes of subgroups — too many to draw. Only its 34 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. C22×PSU(3,𝔽2) | C2 | semidirect |
| 2. C2×AΓL(1,𝔽9) | C2 | semidirect |
| 4. C22⋊AGL(1,𝔽9) | C2 | semidirect |
| 5. PSU(3,𝔽2)⋊C4 | C2 | semidirect |
| 26. PSU(3,𝔽2) | D4 | semidirect |
| 34. C22×C32 | SD16 | semidirect |
| 37. C2×C3⋊D3 | SD16 | semidirect |
| 86. C32 | #448 | semidirect |
| 116. C22 | AΓL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×PSU(3,𝔽2) | 2 |
| C2×AΓL(1,𝔽9) | 2 |
| #64242 | 2 |
| C22⋊AGL(1,𝔽9) | 2 |
| PSU(3,𝔽2)⋊C4 | 2 |
| #448 | 9 |