Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
254 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 48 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 | #4207⋊C3 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624891 | C2 |
| prime radical | #92304 | C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624891 | C2 | semidirect |
| 2. #92311 | C3 | semidirect |
| 3. #92308 | C3 | semidirect |
| 4. #6895⋊C2 | C3 | semidirect |
| 14. #6898 | C2×C3 | semidirect |
| 19. #6896 | C2×C3 | semidirect |
| 22. #6895 | C2×C3 | semidirect |
| 30. C9×3−1+2 | D3 | semidirect |
| 31. C9×3−1+2 | D3 | semidirect |
| 33. C3×C9⋊C9 | D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624891 | 2 |
| #92311 | 3 |
| #92308 | 3 |
| #6895⋊C2 | 3 |
| #92304 | 3 |
| C9×AGL(1,ℤ/9) | 3 |
| C9×(C3⋊D3)⋊C3 | 3 |
| C3×D9⋊C9 | 3 |