Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
227 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 227 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 7. #5021 | C3 | direct (N × H) |
| 29. C32×Q8 | Q8 | semidirect |
| 80. C3×Q8 | Dic6 | semidirect |
| 81. C3×Q8 | C3×Q8 | semidirect |
| 137. C32 | #477 | semidirect |
| 140. Q8 | C3×Dic6 | semidirect |
| 166. C3 | #5021 | direct (N × H) |
| 167. C3 | C3×#477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q8 | 2 |
| C3×#869 | 2 |
| C3×#835 | 2 |
| C3×#807 | 2 |
| C3×C4⋊(C3⋊C8) | 2 |
| C3×#477 | 3 |
| #5021 | 3 |