Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
282 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C3×#216 | C2 | semidirect |
| 6. C2×C3×Dic12 | C2 | semidirect |
| 7. C3×#815 | C2 | semidirect |
| 9. #5167 | C3 | direct (N × H) |
| 31. #944 | C2×C3 | semidirect |
| 32. C2×#216 | C2×C3 | semidirect |
| 35. C2×Dic12 | C2×C3 | semidirect |
| 37. #815 | C2×C3 | semidirect |
| 181. C32 | #497 | semidirect |
| 217. C3 | #5167 | direct (N × H) |
| 218. C3 | C3×#497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×SD16 | 2 |
| C3×#944 | 2 |
| C2×C3×#216 | 2 |
| C3×#936 | 2 |
| C2×C3×#214 | 2 |
| C2×C3×Dic12 | 2 |
| C3×#815 | 2 |
| C3×#497 | 3 |
| #5167 | 3 |