Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
725 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 725 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
| 3. C32×D3×C9 | C3 | semidirect |
| 5. D3×C32⋊C9 | C3 | semidirect |
| 7. C33×C9 | C2×C3 | semidirect |
| 11. C9×H(3,𝔽3) | D3 | direct (N × H) |
| 12. C3×C32⋊C9 | C2×C3 | semidirect |
| 16. D3×H(3,𝔽3) | C9 | direct (N × H) |
| 24. C3×H(3,𝔽3) | C2×C9 | semidirect |
| 31. C32×C9 | C3×D3 | semidirect |
| 36. C32⋊C9 | C3×D3 | semidirect |
| 40. C32×D3 | C3×C9 | semidirect |
| 47. D3×C9 | H(3,𝔽3) | direct (N × H) |
| 54. C33 | C2×C3×C9 | semidirect |
| 58. H(3,𝔽3) | D3×C9 | direct (N × H) |
| 68. C3×C9 | C2×H(3,𝔽3) | semidirect |
| 93. C32 | C3×D3×C9 | semidirect |
| 101. C9 | D3×H(3,𝔽3) | direct (N × H) |
| 106. D3 | C9×H(3,𝔽3) | direct (N × H) |
| 112. 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×H(3,𝔽3) | 3 |
| C32×D3×C9 | 3 |
| C2×C9×H(3,𝔽3) | 3 |
| D3×C32⋊C9 | 3 |