Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
526 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 198 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×#936 | C2 | semidirect |
| 3. C3×#935 | C2 | semidirect |
| 4. C3×D4×Dic3 | C2 | semidirect |
| 5. C3×C4×Dic6 | C2 | semidirect |
| 7. #5713 | C3 | direct (N × H) |
| 25. #936 | C2×C3 | semidirect |
| 26. #935 | C2×C3 | semidirect |
| 27. D4×Dic3 | C2×C3 | semidirect |
| 28. C4×Dic6 | C2×C3 | semidirect |
| 129. C32 | #559 | semidirect |
| 156. C3 | #5713 | direct (N × H) |
| 157. C3 | C3×#559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#127 | 2 |
| C3×#936 | 2 |
| C3×#935 | 2 |
| C3×D4×Dic3 | 2 |
| C3×C4×Dic6 | 2 |
| C3×#559 | 3 |
| #5713 | 3 |