Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
323 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 323 conjugacy classes of subgroups — too many to draw. Only its 102 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×D3×M16 | C2 | semidirect |
| 3. C32×#100 | C2 | semidirect |
| 4. C3×#833 | C2 | semidirect |
| 5. C3×#824 | C2 | semidirect |
| 7. #4745 | C3 | direct (N × H) |
| 22. D3×M16 | C2×C3 | semidirect |
| 26. C3×#100 | D3 | semidirect |
| 27. C3×#100 | C2×C3 | semidirect |
| 28. #833 | C2×C3 | semidirect |
| 29. #824 | C2×C3 | semidirect |
| 82. #100 | C3×D3 | semidirect |
| 152. C32 | #413 | semidirect |
| 188. C3 | #4745 | direct (N × H) |
| 189. C3 | C3×#413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#237 | 2 |
| C3×D3×M16 | 2 |
| C32×#100 | 2 |
| C3×#833 | 2 |
| C3×#824 | 2 |
| C3×#413 | 3 |
| #4745 | 3 |