Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
308 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 93 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×Dic3×D9 | C2 | semidirect |
| 3. C4⋊(C3⋊Dic9) | C2 | semidirect |
| 4. C4×C9×Dic3 | C2 | semidirect |
| 5. (C2×D9)⋊Dic3 | C2 | semidirect |
| 13. C3×D36 | C4 | semidirect |
| 29. C2×C3×D9 | C2×C4 | semidirect |
| 30. C3×C4×C9 | C2×C4 | semidirect |
| 33. C9×Dic3 | D4 | semidirect |
| 50. D36 | Dic3 | direct (N × H) |
| 66. C4×Dic3 | D9 | semidirect |
| 79. C2×D9 | C2×Dic3 | semidirect |
| 83. C4×C9 | C2×Dic3 | semidirect |
| 87. C3×C9 | C4×D4 | semidirect |
| 132. C3×C4 | C4×D9 | semidirect |
| 138. Dic3 | D36 | direct (N × H) |
| 141. C9 | D4×Dic3 | semidirect |
| 167. C4 | Dic3×D9 | semidirect |
| 169. C3 | C4×D36 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D36 | 2 |
| C2×Dic3×D9 | 2 |
| C4⋊(C3⋊Dic9) | 2 |
| C4×C9×Dic3 | 2 |
| (C2×D9)⋊Dic3 | 2 |
| Dic3×D12 | 3 |
| C4×D36 | 3 |