Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
229 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 229 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. C32×#103 | C2 | semidirect |
| 4. C3×#835 | C2 | semidirect |
| 6. C3×#818 | C2 | semidirect |
| 7. C3×#807 | C2 | semidirect |
| 9. #4811 | C3 | direct (N × H) |
| 29. C3×#103 | D3 | semidirect |
| 30. C3×#103 | C2×C3 | semidirect |
| 32. #835 | C2×C3 | semidirect |
| 34. #818 | C2×C3 | semidirect |
| 35. #807 | C2×C3 | semidirect |
| 92. #103 | C3×D3 | semidirect |
| 170. C32 | #484 | semidirect |
| 208. C3 | #4811 | direct (N × H) |
| 209. C3 | C3×#484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#946 | 2 |
| C3×D3×C4⋊C4 | 2 |
| C32×#103 | 2 |
| C3×#835 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#818 | 2 |
| C3×#807 | 2 |
| C3×#484 | 3 |
| #4811 | 3 |