Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
262 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 87 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 | semidirect |
| 5. Dic3×Dic9 | C2 | semidirect |
| 11. C2×C3×Dic9 | C4 | semidirect |
| 45. C2×Dic9 | Dic3 | semidirect |
| 81. C3×C9 | #117 | semidirect |
| 130. C9 | #926 | semidirect |
| 154. C3 | #63439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic9 | 2 |
| #88551 | 2 |
| C9×#217 | 2 |
| Dic9⋊Dic3 | 2 |
| Dic3×Dic9 | 2 |
| #63955 | 3 |
| #63439 | 3 |