Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
169 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 169 conjugacy classes of subgroups — too many to draw. Only its 62 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×C3×C4×D3 | C2 | semidirect |
| 3. C32×C4⋊C4 | C2 | semidirect |
| 4. C3×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C3×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C3×Dic3⋊C4 | C2 | semidirect |
| 9. #894 | C3 | direct (N × H) |
| 22. C2×C4×D3 | C2×C3 | semidirect |
| 25. C3×C4⋊C4 | D3 | semidirect |
| 26. C3×C4⋊C4 | C2×C3 | semidirect |
| 30. (C2×D3)⋊C4 | C2×C3 | semidirect |
| 31. (C2×D3)⋊C4 | C2×C3 | semidirect |
| 32. (C2×D3)⋊C4 | C2×C3 | semidirect |
| 33. Dic3⋊C4 | C2×C3 | semidirect |
| 76. C4⋊C4 | C3×D3 | semidirect |
| 108. C32 | #123 | semidirect |
| 144. C3 | #894 | direct (N × H) |
| 145. C3 | C3×#123 | 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×C3×C4×D3 | 2 |
| C32×C4⋊C4 | 2 |
| C3×(C2×D3)⋊C4 | 2 |
| C3×Dic3⋊C4 | 2 |
| C3×#123 | 3 |
| #894 | 3 |