Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
737 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 737 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
| 6. C33×C9 | D3 | semidirect |
| 8. C9×H(3,𝔽3) | D3 | semidirect |
| 11. C3⋊#272 | C9 | direct (N × H) |
| 19. C3×H(3,𝔽3) | C2×C9 | semidirect |
| 26. C32×C9 | C3⋊D3 | semidirect |
| 43. C33 | D3×C9 | semidirect |
| 47. H(3,𝔽3) | D3×C9 | semidirect |
| 55. C3×C9 | #272 | semidirect |
| 79. C32 | C9×C3⋊D3 | semidirect |
| 85. C9 | C3⋊#272 | direct (N × H) |
| 96. C3 | C9×#272 | 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⋊#272 | 3 |
| C3×C9×C3⋊D3 | 3 |
| C9×#272 | 3 |