Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
668 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 180 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×D3×C3⋊Dic3 | C2 | semidirect |
| 3. C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 4. C3×C4×C3⋊Dic3 | C2 | semidirect |
| 5. (C2×D3)⋊(C3⋊Dic3) | C2 | semidirect |
| 13. C32×D12 | C4 | semidirect |
| 23. C4×C3⋊Dic3 | D3 | semidirect |
| 29. C2×C32×D3 | C2×C4 | semidirect |
| 30. C33×C4 | C2×C4 | semidirect |
| 33. C3×C3⋊Dic3 | D4 | semidirect |
| 50. C3×D12 | Dic3 | semidirect |
| 75. C2×C3×D3 | C2×Dic3 | semidirect |
| 77. C32×C4 | C4×D3 | semidirect |
| 78. C32×C4 | C2×Dic3 | semidirect |
| 83. C3⋊Dic3 | D12 | direct (N × H) |
| 87. C33 | C4×D4 | semidirect |
| 102. D12 | C3⋊Dic3 | direct (N × H) |
| 128. C2×D3 | C2×C3⋊Dic3 | semidirect |
| 132. C3×C4 | D3×Dic3 | semidirect |
| 133. C3×C4 | C2×C3⋊Dic3 | semidirect |
| 140. C32 | C4×D12 | semidirect |
| 141. C32 | D4×Dic3 | semidirect |
| 167. C4 | D3×C3⋊Dic3 | semidirect |
| 169. C3 | Dic3×D12 | semidirect |
| 170. C3 | D4×C3⋊Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D12 | 2 |
| C2×D3×C3⋊Dic3 | 2 |
| C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C3×C4×C3⋊Dic3 | 2 |
| (C2×D3)⋊(C3⋊Dic3) | 2 |
| D4×C3⋊Dic3 | 3 |
| Dic3×D12 | 3 |