Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
321 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 321 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 |
|---|---|---|
| 2. C9⋊#859 | C2 | semidirect |
| 6. C9×#41⋊C3 | C4 | semidirect |
| 20. C9×SL(2,𝔽3) | C2×C4 | semidirect |
| 27. C9×#41 | Dic3 | semidirect |
| 32. #41⋊C9 | Dic3 | semidirect |
| 77. #41⋊C3 | Dic9 | semidirect |
| 117. SL(2,𝔽3) | C2×Dic9 | semidirect |
| 130. #41 | C3⋊Dic9 | semidirect |
| 152. C9 | #5426 | semidirect |
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 |
| #10593660 | 3 |
| #10589528 | 3 |
| #10588916 | 3 |
| C4⋊(C3⋊Dic9) | 4 |