Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
195 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×C3×Dic12 | C2 | semidirect |
| 3. C3×#829 | C2 | semidirect |
| 4. C3×#827 | C2 | semidirect |
| 5. C3×#812 | C2 | semidirect |
| 7. #5195 | C3 | direct (N × H) |
| 21. C2×Dic12 | C2×C3 | semidirect |
| 25. #829 | C2×C3 | semidirect |
| 26. #827 | C2×C3 | semidirect |
| 27. #812 | C2×C3 | semidirect |
| 129. C32 | #510 | semidirect |
| 156. C3 | #5195 | direct (N × H) |
| 157. C3 | C3×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#135 | 2 |
| C2×C3×Dic12 | 2 |
| C3×#829 | 2 |
| C3×#827 | 2 |
| C3×#812 | 2 |
| C3×#510 | 3 |
| #5195 | 3 |