Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
205 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 205 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. C22×C3×Dic3 | C2 | semidirect |
| 3. C2×C3×C4×D3 | C2 | semidirect |
| 4. C32×C22⋊C4 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C3×Dic3⋊C4 | C2 | semidirect |
| 7. C3×C4×Dic3 | C2 | semidirect |
| 9. #67⋊C4 | C3 | direct (N × H) |
| 14. C3×#67 | C4 | semidirect |
| 24. C22×Dic3 | C2×C3 | semidirect |
| 25. C2×C4×D3 | C2×C3 | semidirect |
| 29. C3×C22⋊C4 | D3 | semidirect |
| 30. C3×C22⋊C4 | C2×C3 | semidirect |
| 32. (C2×D3)⋊C4 | C2×C3 | semidirect |
| 33. Dic3⋊C4 | C2×C3 | semidirect |
| 34. C4×Dic3 | C2×C3 | semidirect |
| 37. C22×C32 | C2×C4 | semidirect |
| 41. C2×C3×D3 | C2×C4 | semidirect |
| 45. C3×Dic3 | C2×C4 | semidirect |
| 46. C3×Dic3 | D4 | semidirect |
| 65. #67 | C3×C4 | semidirect |
| 81. C22⋊C4 | C3×D3 | semidirect |
| 94. C22×C3 | C4×D3 | semidirect |
| 95. C22×C3 | C2×C3×C4 | semidirect |
| 100. C2×D3 | C2×C3×C4 | semidirect |
| 111. Dic3 | C2×C3×C4 | semidirect |
| 112. Dic3 | C3×D4 | semidirect |
| 113. C32 | C4×D4 | semidirect |
| 143. C22 | C3×C4×D3 | semidirect |
| 151. C3 | #67⋊C4 | direct (N × H) |
| 152. 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×#67 | 2 |
| C22×C3×Dic3 | 2 |
| C2×C3×C4×D3 | 2 |
| C32×C22⋊C4 | 2 |
| C3×(C2×D3)⋊C4 | 2 |
| C3×Dic3⋊C4 | 2 |
| C3×C4×Dic3 | 2 |
| C3×C4×D4 | 3 |
| #67⋊C4 | 3 |