Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
282 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 3. C9×C4⋊Dic3 | C2 | semidirect |
| 4. C4×C9×Dic3 | C2 | semidirect |
| 8. C2×C3×C4×C9 | C4 | semidirect |
| 28. #926 | C9 | direct (N × H) |
| 40. C2×C4×C9 | Dic3 | semidirect |
| 53. C4⋊Dic3 | C2×C9 | semidirect |
| 54. C4×Dic3 | C2×C9 | semidirect |
| 73. C3×C9 | #117 | semidirect |
| 81. C2×C3×C4 | C4×C9 | semidirect |
| 120. C9 | #926 | direct (N × H) |
| 123. C2×C4 | C9×Dic3 | semidirect |
| 142. C3 | C9×#117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C9 | 2 |
| C9×#217 | 2 |
| C9×C4⋊Dic3 | 2 |
| C4×C9×Dic3 | 2 |
| C3×#926 | 3 |
| C9×#117 | 3 |