Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
288 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 288 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. C22×C9×Dic3 | C2 | semidirect |
| 3. C9×#217 | C2 | semidirect |
| 4. C9×#217 | C2 | semidirect |
| 5. C9×Dic3⋊C4 | C2 | semidirect |
| 35. #935 | C9 | direct (N × H) |
| 62. C22×Dic3 | C2×C9 | semidirect |
| 66. #217 | C2×C9 | semidirect |
| 67. #217 | C2×C9 | semidirect |
| 68. Dic3⋊C4 | C2×C9 | semidirect |
| 92. C3×C9 | #123 | semidirect |
| 152. C9 | #935 | direct (N × H) |
| 181. C3 | C9×#123 | 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 |
| C22×C9×Dic3 | 2 |
| C9×#217 | 2 |
| C9×Dic3⋊C4 | 2 |
| C3×#935 | 3 |
| C9×#123 | 3 |