Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
386 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C9 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624883 | C2 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624883 | C2 | semidirect |
| 3. #92303 | C3 | semidirect |
| 4. C3⋊#4169 | C3 | semidirect |
| 10. C9⋊H(3,𝔽3) | C2×C3 | semidirect |
| 12. #6891 | D3 | semidirect |
| 14. C3×C32⋊C9 | C2×C3 | semidirect |
| 17. C3⋊(C3⋊D9) | C32 | semidirect |
| 30. C3×3−1+2 | C3×D3 | semidirect |
| 37. C32×C9 | C2×C32 | semidirect |
| 48. C32⋊C9 | C3×D3 | semidirect |
| 75. 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×C3⋊((C3⋊D3)⋊C3) | 3 |
| #92303 | 3 |
| C3⋊#4169 | 3 |
| #4169⋊C3 | 3 |