Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
755 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 755 conjugacy classes of subgroups — too many to draw. Only its 120 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 | C33×C9 | C2×C3 |
| Frattini | C32 | C3×C3⋊(C3⋊D3) |
| Fitting | C3×C9⋊H(3,𝔽3) | C2 |
| socle | C33 | C3×C3⋊D3 |
| LCS | G ▷ C33×C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C9⋊H(3,𝔽3) | C2 | semidirect |
| 2. C3⋊(C3⋊(C3⋊D9)) | C3 | semidirect |
| 8. C32×3−1+2 | D3 | semidirect |
| 10. C33×C9 | C2×C3 | semidirect |
| 12. C9⋊H(3,𝔽3) | D3 | semidirect |
| 15. C3×C32⋊C9 | D3 | semidirect |
| 34. C3×3−1+2 | C3⋊D3 | semidirect |
| 43. C32×C9 | C3×D3 | semidirect |
| 47. C32⋊C9 | C3⋊D3 | semidirect |
| 74. C33 | AGL(1,ℤ/9) | semidirect |
| 89. C3×C9 | (C3⋊D3)⋊C3 | semidirect |
| 122. C32 | C3⋊AGL(1,ℤ/9) | semidirect |
| 128. C9 | C3⋊((C3⋊D3)⋊C3) | semidirect |
| 139. C3 | #92303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9⋊H(3,𝔽3) | 2 |
| C3⋊(C3⋊(C3⋊D9)) | 3 |
| C3⋊(C3⋊AGL(1,ℤ/9)) | 3 |
| C3⋊(C3⋊((C3⋊D3)⋊C3)) | 3 |
| #92303 | 3 |
| C3⋊#4169 | 3 |