Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
234 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 32 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. C9×#997 | C2 | semidirect |
| 3. C9×B(4,𝔽2) | C3 | semidirect |
| 4. B(4,𝔽2)⋊C9 | C3 | semidirect |
| 7. C9×H(5,𝔽2) | C2×C3 | semidirect |
| 8. #63703 | C2×C3 | semidirect |
| 16. B(4,𝔽2)⋊C3 | C9 | direct (N × H) |
| 18. C24×C9 | A4 | semidirect |
| 30. #997 | C2×C9 | semidirect |
| 53. B(4,𝔽2) | C3×C9 | semidirect |
| 80. H(5,𝔽2) | C2×C3×C9 | semidirect |
| 108. C24 | C9×A4 | semidirect |
| 130. C9 | B(4,𝔽2)⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#997 | 2 |
| C3×B(4,𝔽2)⋊C3 | 3 |
| C9×B(4,𝔽2) | 3 |
| B(4,𝔽2)⋊C9 | 3 |
| C22×C9×A4 | 4 |