Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
330 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 4. Dic9⋊Dic3 | C2 | direct (N × H) |
| 12. C2×C3×Dic9 | C4 | semidirect |
| 29. C3×Dic9 | C2×C4 | semidirect |
| 47. C2×Dic9 | Dic3 | semidirect |
| 49. C2×C3×C9 | C4⋊C4 | semidirect |
| 80. Dic9 | C2×Dic3 | semidirect |
| 82. C3×C9 | C2×C4⋊C4 | semidirect |
| 108. C2×C9 | C4⋊Dic3 | semidirect |
| 137. C9 | C2×C4⋊Dic3 | semidirect |
| 149. C2×C3 | Dic9⋊C4 | semidirect |
| 165. C3 | C2×Dic9⋊C4 | semidirect |
| 167. C2 | Dic9⋊Dic3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊Dic9 | 2 |
| C22×C9×Dic3 | 2 |
| C22×C3×Dic9 | 2 |
| Dic9⋊Dic3 | 2 |
| C2×Dic3⋊Dic3 | 3 |
| C2×Dic9⋊C4 | 3 |