Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
497 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 497 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
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⋊AGL(1,ℤ/9) | C3 | semidirect |
| 4. C32×C3⋊D9 | C3 | semidirect |
| 6. C32×3−1+2 | C2×C3 | semidirect |
| 8. C33×C9 | C2×C3 | semidirect |
| 11. C9⋊H(3,𝔽3) | D3 | semidirect |
| 29. C3×3−1+2 | C3×D3 | semidirect |
| 41. C32×C9 | C3×D3 | semidirect |
| 55. C3⋊D9 | H(3,𝔽3) | semidirect |
| 69. C33 | AGL(1,ℤ/9) | semidirect |
| 94. C3×C9 | C2×H(3,𝔽3) | semidirect |
| 128. C32 | C3⋊AGL(1,ℤ/9) | semidirect |
| 133. C9 | D3×H(3,𝔽3) | semidirect |
| 146. C3 | D9⋊H(3,𝔽3) | 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⋊AGL(1,ℤ/9) | 3 |
| C3⋊D3×H(3,𝔽3) | 3 |
| C32×C3⋊D9 | 3 |
| D9⋊H(3,𝔽3) | 3 |