Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
263 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 263 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. C9×#859 | C2 | semidirect |
| 5. C9×#41⋊C3 | C4 | semidirect |
| 18. C9×SL(2,𝔽3) | C2×C4 | semidirect |
| 19. #5426 | C9 | direct (N × H) |
| 25. C9×#41 | Dic3 | semidirect |
| 44. #859 | C2×C9 | semidirect |
| 75. #41⋊C3 | C4×C9 | semidirect |
| 117. SL(2,𝔽3) | C2×C4×C9 | semidirect |
| 130. #41 | C9×Dic3 | semidirect |
| 154. C9 | #5426 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#41⋊C3 | 2 |
| C9×#859 | 2 |
| C3×#5426 | 3 |
| C9×#417 | 3 |
| C9×C4⋊Dic3 | 4 |