Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
275 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 52 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 | #4169 |
| commutator, hypocenter | C3×C9 | C2×C3×C9 |
| Frattini, socle | C33 | C32×D3 |
| Fitting | C9×C32⋊C9 | C2 |
| prime radical | C3×#4169 | 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×C32⋊C9 | C2 | semidirect |
| 3. C9×C3⋊D9 | C3 | semidirect |
| 5. #92158 | C3 | semidirect |
| 10. C3×C92 | C2×C3 | semidirect |
| 12. #6855 | C2×C3 | semidirect |
| 20. #4169 | C9 | direct (N × H) |
| 33. C32×C9 | D9 | semidirect |
| 39. C32⋊C9 | C2×C9 | semidirect |
| 50. C3⋊D9 | C3×C9 | semidirect |
| 97. C3×C9 | C2×C3×C9 | semidirect |
| 121. C32 | C9×D9 | semidirect |
| 136. C9 | #4169 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C32⋊C9 | 2 |
| C3×C9×C3⋊D3 | 3 |
| C9×C3⋊D9 | 3 |
| C3×#4169 | 3 |
| #92158 | 3 |