Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
258 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 95 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. C4×C3⋊Dic9 | C2 | semidirect |
| 3. C3×C4×Dic9 | C2 | semidirect |
| 5. Dic3⋊Dic9 | C2 | semidirect |
| 13. C4×D3×C9 | C4 | semidirect |
| 24. C4×Dic9 | D3 | semidirect |
| 80. C3×C9 | #117 | semidirect |
| 94. C4×D3 | Dic9 | semidirect |
| 127. C9 | #872 | semidirect |
| 150. C3 | #63488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×C9 | 2 |
| C4×C3⋊Dic9 | 2 |
| C3×C4×Dic9 | 2 |
| (C2×D3)⋊Dic9 | 2 |
| Dic3⋊Dic9 | 2 |
| #63855 | 3 |
| #63488 | 3 |