Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
303 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 303 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×#944 | C2 | semidirect |
| 3. C3×#909 | C2 | semidirect |
| 4. C32×#101 | C2 | semidirect |
| 5. C3×#825 | C2 | semidirect |
| 7. #4752 | C3 | direct (N × H) |
| 23. #944 | C2×C3 | semidirect |
| 24. #909 | C2×C3 | semidirect |
| 27. C3×#101 | D3 | semidirect |
| 28. C3×#101 | C2×C3 | semidirect |
| 29. #825 | C2×C3 | semidirect |
| 80. #101 | C3×D3 | semidirect |
| 144. C32 | #456 | semidirect |
| 175. C3 | #4752 | direct (N × H) |
| 176. C3 | C3×#456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1007 | 2 |
| C3×#944 | 2 |
| C3×#909 | 2 |
| C32×#101 | 2 |
| C3×#825 | 2 |
| C3×#456 | 3 |
| #4752 | 3 |