Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
329 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 329 conjugacy classes of subgroups — too many to draw. Only its 66 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. #63871 | C2 | semidirect |
| 4. C2×#3715 | C2 | semidirect |
| 5. #63647 | C2 | semidirect |
| 6. C3×#821 | C2 | semidirect |
| 7. #63565 | C2 | semidirect |
| 31. C2×Dic12 | D3 | semidirect |
| 35. #821 | D3 | semidirect |
| 211. C32 | #452 | semidirect |
| 259. C3 | #4783 | semidirect |
| 260. C3 | #5187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3796 | 2 |
| C2×C3×Dic12 | 2 |
| #63871 | 2 |
| C2×#3715 | 2 |
| #63647 | 2 |
| C3×#821 | 2 |
| #63565 | 2 |
| #5187 | 3 |
| #4783 | 3 |