Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
329 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 329 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×#924 | C2 | semidirect |
| 3. C2×C3×Dic12 | C2 | semidirect |
| 4. C2×C3×#204 | C2 | semidirect |
| 5. C32×C22⋊C8 | C2 | semidirect |
| 6. C3×#821 | C2 | semidirect |
| 7. C3×#816 | C2 | semidirect |
| 9. #4733 | C3 | direct (N × H) |
| 30. #924 | C2×C3 | semidirect |
| 31. C2×Dic12 | C2×C3 | semidirect |
| 32. C2×#204 | C2×C3 | semidirect |
| 36. C3×C22⋊C8 | D3 | semidirect |
| 37. C3×C22⋊C8 | C2×C3 | semidirect |
| 38. #821 | C2×C3 | semidirect |
| 39. #816 | C2×C3 | semidirect |
| 112. C22⋊C8 | C3×D3 | semidirect |
| 211. C32 | #452 | semidirect |
| 259. C3 | #4733 | direct (N × H) |
| 260. C3 | C3×#452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#235 | 2 |
| C3×#924 | 2 |
| C2×C3×Dic12 | 2 |
| C2×C3×#204 | 2 |
| C32×C22⋊C8 | 2 |
| C3×#821 | 2 |
| C3×#816 | 2 |
| C3×#452 | 3 |
| #4733 | 3 |