Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
203 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 203 conjugacy classes of subgroups — too many to draw. Only its 90 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×C42 | C2 | semidirect |
| 4. C3×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C3×C4⋊Dic3 | C2 | semidirect |
| 7. C4×D12 | C3 | direct (N × H) |
| 13. C3×D12 | C4 | direct (N × H) |
| 18. C2×C4×D3 | C2×C3 | semidirect |
| 22. C3×C42 | D3 | semidirect |
| 23. C3×C42 | C2×C3 | semidirect |
| 24. (C2×D3)⋊C4 | C2×C3 | semidirect |
| 25. C4⋊Dic3 | C2×C3 | semidirect |
| 29. C2×C3×D3 | C2×C4 | semidirect |
| 31. C32×C4 | C2×C4 | semidirect |
| 32. C32×C4 | D4 | semidirect |
| 50. D12 | C3×C4 | direct (N × H) |
| 60. C42 | C3×D3 | semidirect |
| 69. C2×D3 | C2×C3×C4 | semidirect |
| 76. C3×C4 | C4×D3 | semidirect |
| 77. C3×C4 | D12 | direct (N × H) |
| 78. C3×C4 | C2×C3×C4 | semidirect |
| 79. C3×C4 | C3×D4 | semidirect |
| 81. C32 | C4×D4 | semidirect |
| 106. C4 | C3×C4×D3 | semidirect |
| 107. C4 | C3×D12 | direct (N × H) |
| 109. C3 | C4×D12 | direct (N × H) |
| 110. C3 | C3×C4×D4 | 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×C42 | 2 |
| C3×(C2×D3)⋊C4 | 2 |
| C3×C4⋊Dic3 | 2 |
| C3×C4×D4 | 3 |
| C4×D12 | 3 |