Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
311 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 311 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. C32×#101 | C2 | semidirect |
| 4. C3×#836 | C2 | semidirect |
| 5. C3×#824 | C2 | semidirect |
| 7. D3×#101 | C3 | direct (N × H) |
| 26. C3×#101 | D3 | direct (N × H) |
| 27. C3×#101 | C2×C3 | semidirect |
| 28. #836 | C2×C3 | semidirect |
| 29. #824 | C2×C3 | semidirect |
| 81. #101 | C3×D3 | direct (N × H) |
| 117. C3×D3 | #101 | direct (N × H) |
| 148. C32 | C2×#101 | semidirect |
| 172. D3 | C3×#101 | direct (N × H) |
| 182. C3 | D3×#101 | direct (N × H) |
| 183. C3 | C2×C3×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×Q8 | 2 |
| C3×D3×M16 | 2 |
| C32×#101 | 2 |
| C3×#836 | 2 |
| C3×#824 | 2 |
| C2×C3×#101 | 3 |
| D3×#101 | 3 |