Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
282 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 1. C2×C3×Dic12 | C2 | semidirect |
| 3. C2×C3×#204 | C2 | semidirect |
| 4. C3×#875 | C2 | semidirect |
| 5. C32×C4×C8 | C2 | semidirect |
| 7. #4696 | C3 | direct (N × H) |
| 21. C2×Dic12 | C2×C3 | semidirect |
| 23. C2×#204 | C2×C3 | semidirect |
| 24. #875 | C2×C3 | semidirect |
| 26. C3×C4×C8 | D3 | semidirect |
| 27. C3×C4×C8 | C2×C3 | semidirect |
| 71. C4×C8 | C3×D3 | semidirect |
| 126. C32 | #495 | semidirect |
| 153. C3 | #4696 | direct (N × H) |
| 154. C3 | C3×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| C2×C3×D24 | 2 |
| C2×C3×#204 | 2 |
| C3×#875 | 2 |
| C32×C4×C8 | 2 |
| C3×#495 | 3 |
| #4696 | 3 |