Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
194 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×#829 | C2 | direct (N × H) |
| 6. C2×#829 | C3 | direct (N × H) |
| 22. #829 | C2×C3 | direct (N × H) |
| 87. C2×C32 | Q32 | semidirect |
| 111. C32 | C2×Q32 | semidirect |
| 123. C2×C3 | #829 | direct (N × H) |
| 124. C2×C3 | C3×Q32 | semidirect |
| 133. C3 | C2×#829 | direct (N × H) |
| 134. C3 | C2×C3×Q32 | semidirect |
| 135. C2 | C3×#829 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q16 | 2 |
| C2×C3×Dic12 | 2 |
| C3×#829 | 2 |
| C2×C3×C3⋊C16 | 2 |
| C2×C3×Q32 | 3 |
| C2×#829 | 3 |