Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
201 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 86 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×C4×Dic3 | C2 | semidirect |
| 7. #893 | C3 | direct (N × H) |
| 13. C3×D12 | C4 | semidirect |
| 18. C2×C4×D3 | C2×C3 | semidirect |
| 20. C3×C4⋊C4 | D3 | semidirect |
| 21. C3×C4⋊C4 | 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 |
| 33. C3×Dic3 | D4 | semidirect |
| 49. D12 | C3×C4 | semidirect |
| 57. C4⋊C4 | C3×D3 | semidirect |
| 68. C2×D3 | C2×C3×C4 | semidirect |
| 75. C3×C4 | C4×D3 | semidirect |
| 76. C3×C4 | C2×C3×C4 | semidirect |
| 78. Dic3 | C3×D4 | semidirect |
| 79. C32 | C4×D4 | semidirect |
| 105. C4 | C3×C4×D3 | semidirect |
| 107. C3 | #893 | direct (N × H) |
| 108. 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×C4⋊C4 | 2 |
| C3×(C2×D3)⋊C4 | 2 |
| C3×C4×Dic3 | 2 |
| C3×C4×D4 | 3 |
| #893 | 3 |