Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
146 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 44 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. D3×Dic6 | C2 | semidirect |
| 3. #3744 | C2 | semidirect |
| 4. C3×#204 | C2 | semidirect |
| 5. C3×D3×C8 | C2 | semidirect |
| 6. #3717 | C2 | semidirect |
| 7. #3716 | C2 | semidirect |
| 12. #634 | C22 | semidirect |
| 15. C3×Dic6 | C22 | semidirect |
| 19. C32×C8 | C22 | semidirect |
| 20. C3×C3⋊C8 | C22 | semidirect |
| 34. #204 | D3 | direct (N × H) |
| 35. D3×C8 | D3 | semidirect |
| 64. Dic6 | C2×D3 | semidirect |
| 67. C3×C8 | C2×D3 | semidirect |
| 68. C3×C8 | C2×D3 | semidirect |
| 69. C3⋊C8 | C2×D3 | semidirect |
| 73. C3×D3 | SD16 | semidirect |
| 100. C32 | C2×SD16 | semidirect |
| 111. C8 | D32 | semidirect |
| 121. D3 | #204 | direct (N × H) |
| 131. C3 | C2×#204 | semidirect |
| 132. C3 | D3×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×D12 | 2 |
| D3×Dic6 | 2 |
| #3744 | 2 |
| C3×#204 | 2 |
| C3×D3×C8 | 2 |
| #3717 | 2 |
| #3716 | 2 |
| D3×SD16 | 3 |
| C2×#204 | 3 |