Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
266 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4169⋊C3 |
| commutator, hypocenter | C3×C9 | C2×C3×C9 |
| Frattini, socle | C33 | C32×D3 |
| Fitting | #10624558 | C2 |
| prime radical | C3×C3⋊AGL(1,ℤ/9) | C3 |
| cosocle | C32×C9 | C2×C32 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624558 | C2 | semidirect |
| 4. #92158 | C3 | semidirect |
| 9. #6855 | C2×C3 | semidirect |
| 11. C3⋊AGL(1,ℤ/9) | C9 | semidirect |
| 22. C3×3−1+2 | C2×C9 | semidirect |
| 38. C3⋊D9 | C3×C9 | semidirect |
| 72. C3×C9 | AGL(1,ℤ/9) | semidirect |
| 73. C3×C9 | C2×C3×C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624558 | 2 |
| C3×C3⋊AGL(1,ℤ/9) | 3 |
| C3×C9×C3⋊D3 | 3 |
| #92158 | 3 |