Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
235 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 90 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×#869 | C2 | semidirect |
| 3. C32×C4⋊C8 | C2 | semidirect |
| 5. C3×#817 | C2 | semidirect |
| 7. #4842 | C3 | direct (N × H) |
| 20. #869 | C2×C3 | semidirect |
| 23. C3×C4⋊C8 | D3 | semidirect |
| 24. C3×C4⋊C8 | C2×C3 | semidirect |
| 27. #817 | C2×C3 | semidirect |
| 35. C3×D12 | Q8 | semidirect |
| 73. C4⋊C8 | C3×D3 | semidirect |
| 95. D12 | C3×Q8 | semidirect |
| 139. C32 | #476 | semidirect |
| 173. C3 | #4842 | direct (N × H) |
| 174. C3 | C3×#476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D12 | 2 |
| C3×#869 | 2 |
| C32×C4⋊C8 | 2 |
| C3×#821 | 2 |
| C3×#817 | 2 |
| C3×#476 | 3 |
| #4842 | 3 |