Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
223 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 223 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. C3×#870 | C2 | semidirect |
| 3. C32×C4⋊C8 | C2 | semidirect |
| 6. C3×#818 | C2 | semidirect |
| 7. C3×#817 | C2 | semidirect |
| 9. #4847 | C3 | direct (N × H) |
| 24. #870 | C2×C3 | semidirect |
| 28. C3×C4⋊C8 | D3 | semidirect |
| 29. C3×C4⋊C8 | C2×C3 | semidirect |
| 34. #818 | C2×C3 | semidirect |
| 35. #817 | C2×C3 | semidirect |
| 89. C4⋊C8 | C3×D3 | semidirect |
| 163. C32 | #478 | semidirect |
| 199. C3 | #4847 | direct (N × H) |
| 200. C3 | C3×#478 | 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×#870 | 2 |
| C32×C4⋊C8 | 2 |
| C3×#821 | 2 |
| C3×#818 | 2 |
| C3×#817 | 2 |
| C3×#478 | 3 |
| #4847 | 3 |