Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
267 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 267 conjugacy classes of subgroups — too many to draw. Only its 82 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×#204 | C2 | semidirect |
| 3. C3×#875 | C2 | semidirect |
| 4. C3×C4×D12 | C2 | semidirect |
| 5. C32×C4⋊C8 | C2 | semidirect |
| 6. C3×#821 | C2 | semidirect |
| 7. C3×#816 | C2 | semidirect |
| 9. #4844 | C3 | direct (N × H) |
| 28. C2×#204 | C2×C3 | semidirect |
| 29. #875 | C2×C3 | semidirect |
| 30. C4×D12 | C2×C3 | semidirect |
| 32. C3×C4⋊C8 | D3 | semidirect |
| 33. C3×C4⋊C8 | C2×C3 | semidirect |
| 36. #821 | C2×C3 | semidirect |
| 37. #816 | C2×C3 | semidirect |
| 101. C4⋊C8 | C3×D3 | semidirect |
| 190. C32 | #463 | semidirect |
| 234. C3 | #4844 | direct (N × H) |
| 235. C3 | C3×#463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D24 | 2 |
| C2×C3×#204 | 2 |
| C3×#875 | 2 |
| C3×C4×D12 | 2 |
| C32×C4⋊C8 | 2 |
| C3×#821 | 2 |
| C3×#816 | 2 |
| C3×#463 | 3 |
| #4844 | 3 |