Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
291 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 291 conjugacy classes of subgroups — too many to draw. Only its 107 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×#131⋊C3 | C2 | semidirect |
| 4. C9×#568 | C3 | semidirect |
| 5. #568⋊C9 | C3 | semidirect |
| 15. C9×#131 | C2×C3 | semidirect |
| 18. #131⋊C9 | C2×C3 | semidirect |
| 23. #568⋊C3 | C9 | direct (N × H) |
| 54. #131⋊C3 | C2×C9 | semidirect |
| 75. #568 | C3×C9 | semidirect |
| 111. #131 | C2×C3×C9 | semidirect |
| 166. C9 | #568⋊C3 | 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×#131⋊C3 | 2 |
| C3×#568⋊C3 | 3 |
| C9×#568 | 3 |
| #568⋊C9 | 3 |
| C3×C9×M16 | 4 |