Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
282 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×C9×Dic6 | C2 | semidirect |
| 3. C9×#217 | C2 | semidirect |
| 4. C4×C9×Dic3 | C2 | semidirect |
| 29. #936 | C9 | direct (N × H) |
| 52. C2×Dic6 | C2×C9 | semidirect |
| 55. #217 | C2×C9 | semidirect |
| 56. C4×Dic3 | C2×C9 | semidirect |
| 74. C3×C9 | #124 | semidirect |
| 121. C9 | #936 | direct (N × H) |
| 144. C3 | C9×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C9 | 2 |
| C2×C9×Dic6 | 2 |
| C9×#217 | 2 |
| C4×C9×Dic3 | 2 |
| C3×#936 | 3 |
| C9×#124 | 3 |