Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
581 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 581 conjugacy classes of subgroups — too many to draw. Only its 117 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×D3×3−1+2 | C3 | semidirect |
| 4. C32×D3×C9 | C3 | semidirect |
| 6. D3×C32⋊C9 | C3 | semidirect |
| 7. D3×C32⋊C9 | C3 | semidirect |
| 8. C32×3−1+2 | C2×C3 | semidirect |
| 10. C33×C9 | C2×C3 | semidirect |
| 16. C9⋊H(3,𝔽3) | D3 | direct (N × H) |
| 17. C3×C32⋊C9 | C2×C3 | semidirect |
| 18. C3×C32⋊C9 | C2×C3 | semidirect |
| 39. C3×3−1+2 | C3×D3 | semidirect |
| 50. C32×C9 | C3×D3 | semidirect |
| 59. C32⋊C9 | C3×D3 | semidirect |
| 60. C32⋊C9 | C3×D3 | semidirect |
| 68. C32×D3 | 3−1+2 | semidirect |
| 78. D3×C9 | H(3,𝔽3) | semidirect |
| 92. C33 | C2×3−1+2 | semidirect |
| 115. C3×C9 | C2×H(3,𝔽3) | semidirect |
| 156. C32 | D3×3−1+2 | semidirect |
| 166. C9 | D3×H(3,𝔽3) | semidirect |
| 172. D3 | C9⋊H(3,𝔽3) | direct (N × H) |
| 180. C3 | C2×C9⋊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×D3×3−1+2 | 3 |
| C3×D3×H(3,𝔽3) | 3 |
| C32×D3×C9 | 3 |
| C2×C9⋊H(3,𝔽3) | 3 |
| D3×C32⋊C9 | 3 |