Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
231 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 231 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.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92303 |
| commutator, cosocle, hypocenter | C9×H(3,𝔽3) | C2×C3 |
| Frattini | C33 | C3×C3⋊D3 |
| Fitting | #10624794 | C2 |
| socle | C32 | C3⋊((C3⋊D3)⋊C3) |
| LCS | G ▷ C9×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624794 | C2 | semidirect |
| 3. C9⋊#272 | C3 | semidirect |
| 6. C32×3−1+2 | D3 | semidirect |
| 9. C9×H(3,𝔽3) | C2×C3 | semidirect |
| 12. #6866 | D3 | semidirect |
| 68. H(3,𝔽3) | AGL(1,ℤ/9) | semidirect |
| 112. C9 | #4174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624794 | 2 |
| C3×C3⋊AGL(1,ℤ/9) | 3 |
| C9⋊#272 | 3 |
| C3⋊#4174 | 3 |
| #92174 | 3 |