Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
587 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 587 conjugacy classes of subgroups — too many to draw. Only its 77 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×C3⋊D9 | C3 | semidirect |
| 6. C33×C9 | C2×C3 | semidirect |
| 8. C9×H(3,𝔽3) | D3 | semidirect |
| 19. C3×H(3,𝔽3) | D9 | semidirect |
| 26. C32×C9 | C3×D3 | semidirect |
| 35. C3⋊D9 | H(3,𝔽3) | direct (N × H) |
| 43. C33 | C3×D9 | semidirect |
| 49. H(3,𝔽3) | C3⋊D9 | direct (N × H) |
| 59. C3×C9 | C2×H(3,𝔽3) | semidirect |
| 82. C32 | C3×C3⋊D9 | semidirect |
| 86. C9 | D3×H(3,𝔽3) | semidirect |
| 96. 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⋊D3×H(3,𝔽3) | 3 |
| C32×C3⋊D9 | 3 |
| D9×H(3,𝔽3) | 3 |