Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
201 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 72 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×Dic3 | C2 | semidirect |
| 3. C4⋊(C3⋊Dic3) | C2 | semidirect |
| 4. C3×C4×Dic3 | C2 | semidirect |
| 5. (C2×D3)⋊Dic3 | C2 | semidirect |
| 13. C3×D12 | C4 | semidirect |
| 25. C4×Dic3 | D3 | semidirect |
| 29. C2×C3×D3 | C2×C4 | semidirect |
| 30. C32×C4 | C2×C4 | semidirect |
| 33. C3×Dic3 | D4 | semidirect |
| 49. D12 | Dic3 | direct (N × H) |
| 68. C2×D3 | C2×Dic3 | semidirect |
| 72. C3×C4 | C4×D3 | semidirect |
| 73. C3×C4 | C2×Dic3 | semidirect |
| 78. Dic3 | D12 | direct (N × H) |
| 79. C32 | C4×D4 | semidirect |
| 105. C4 | D3×Dic3 | semidirect |
| 107. C3 | C4×D12 | semidirect |
| 108. C3 | D4×Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D12 | 2 |
| C2×D3×Dic3 | 2 |
| C4⋊(C3⋊Dic3) | 2 |
| C3×C4×Dic3 | 2 |
| (C2×D3)⋊Dic3 | 2 |
| D4×Dic3 | 3 |
| C4×D12 | 3 |