Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
356 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #4207 |
| commutator, hypocenter | C3×C9 | C2×C3×C9 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | C9×#737 | C2 |
| prime radical | C3×#4207 | C3 |
| cosocle | C32×C9 | C2×C32 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#737 | C2 | semidirect |
| 3. #92294 | C3 | semidirect |
| 4. C9×C3⋊D9 | C3 | semidirect |
| 14. C9×3−1+2 | D3 | semidirect |
| 19. #6887 | C2×C3 | semidirect |
| 21. C3×C92 | D3 | semidirect |
| 22. C3×C92 | C2×C3 | semidirect |
| 23. #4207 | C9 | direct (N × H) |
| 38. #737 | C2×C9 | semidirect |
| 78. C3⋊D9 | C3×C9 | semidirect |
| 95. 3−1+2 | D3×C9 | semidirect |
| 121. C3×C9 | D3×C9 | semidirect |
| 122. C3×C9 | C2×C3×C9 | semidirect |
| 161. C9 | #4207 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#737 | 2 |
| C3×#4207 | 3 |
| #92294 | 3 |
| C9×C3⋊D9 | 3 |
| C9×AGL(1,ℤ/9) | 3 |
| C9×(C3⋊D3)⋊C3 | 3 |
| C3×C9×D9 | 3 |