Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 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. Dic3×D12 | C2 | semidirect |
| 3. #63644 | C2 | semidirect |
| 4. C3×#815 | C2 | semidirect |
| 5. #63563 | C2 | semidirect |
| 14. C3×D24 | C4 | semidirect |
| 26. #815 | D3 | semidirect |
| 32. C3×D12 | C2×C4 | semidirect |
| 34. C32×C8 | C2×C4 | semidirect |
| 54. D24 | Dic3 | semidirect |
| 82. D12 | C2×Dic3 | semidirect |
| 86. C3×C8 | C4×D3 | semidirect |
| 87. C3×C8 | C2×Dic3 | semidirect |
| 120. C32 | #442 | semidirect |
| 129. C8 | D3×Dic3 | semidirect |
| 147. C3 | #4711 | semidirect |
| 148. C3 | #5152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D24 | 2 |
| Dic3×D12 | 2 |
| #63644 | 2 |
| C3×#815 | 2 |
| #63563 | 2 |
| #5152 | 3 |
| #4711 | 3 |