Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
389 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 389 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 | C3 | C3×C3⋊AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624883 | C2 |
| hypercenter | C32 | C3⋊AGL(1,ℤ/9) |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624883 | C2 | semidirect |
| 3. #92302 | C3 | semidirect |
| 4. C3×#4181 | C3 | semidirect |
| 9. C9⋊H(3,𝔽3) | D3 | semidirect |
| 11. #6891 | C2×C3 | semidirect |
| 13. C3×C32⋊C9 | C2×C3 | semidirect |
| 24. C3×3−1+2 | C3×D3 | semidirect |
| 31. C32×C9 | C3×D3 | semidirect |
| 60. C33 | AGL(1,ℤ/9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624883 | 2 |
| C3⋊D3×H(3,𝔽3) | 3 |
| #92302 | 3 |
| C3×#4181 | 3 |
| D9⋊H(3,𝔽3) | 3 |