Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
203 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 203 conjugacy classes of subgroups — too many to draw. Only its 28 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. Dic3×PSU(3,𝔽2) | C3 | semidirect |
| 4. C3×PSU(3,𝔽2)⋊C3 | C4 | semidirect |
| 19. C3×PSU(3,𝔽2) | C3×C4 | semidirect |
| 21. PSU(3,𝔽2)⋊C3 | Dic3 | direct (N × H) |
| 37. C3⋊(C3⋊Dic3) | SL(2,𝔽3) | semidirect |
| 41. C32×Dic3 | SL(2,𝔽3) | semidirect |
| 53. PSU(3,𝔽2) | C3×Dic3 | semidirect |
| 102. C33 | C4×SL(2,𝔽3) | semidirect |
| 154. Dic3 | PSU(3,𝔽2)⋊C3 | direct (N × H) |
| 165. C32 | Dic3×SL(2,𝔽3) | semidirect |
| 198. C3 | C4×PSU(3,𝔽2)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×PSU(3,𝔽2)⋊C3 | 2 |
| Dic3×PSU(3,𝔽2) | 3 |
| C4×PSU(3,𝔽2)⋊C3 | 3 |
| Dic3×(C3⋊D3)⋊C3 | 4 |
| Dic3×SL(2,𝔽3) | 9 |