Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
306 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 306 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 |
|---|---|---|
| 2. C3×#951 | C2 | semidirect |
| 3. C3×#909 | C2 | semidirect |
| 4. C3×#869 | C2 | semidirect |
| 5. C32×#104 | C2 | semidirect |
| 6. C3×#824 | C2 | semidirect |
| 7. C3×#805 | C2 | semidirect |
| 9. #4826 | C3 | direct (N × H) |
| 32. #951 | C2×C3 | semidirect |
| 33. #909 | C2×C3 | semidirect |
| 34. #869 | C2×C3 | semidirect |
| 37. C3×#104 | D3 | semidirect |
| 38. C3×#104 | C2×C3 | semidirect |
| 40. #824 | C2×C3 | semidirect |
| 41. #805 | C2×C3 | semidirect |
| 117. #104 | C3×D3 | semidirect |
| 217. C32 | #456 | semidirect |
| 262. C3 | #4826 | direct (N × H) |
| 263. C3 | C3×#456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1010 | 2 |
| C3×#951 | 2 |
| C3×#909 | 2 |
| C3×#869 | 2 |
| C32×#104 | 2 |
| C3×#824 | 2 |
| C3×#805 | 2 |
| C3×#456 | 3 |
| #4826 | 3 |