Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
458 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 230 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. #5722 | C3 | direct (N × H) |
| 36. C3×Dic6 | Q8 | semidirect |
| 91. Dic6 | C3×Q8 | semidirect |
| 120. C32 | Q82 | semidirect |
| 142. C3 | #5722 | direct (N × H) |
| 143. C3 | C3×Q82 | 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×#944 | 2 |
| C3×#888 | 2 |
| C3×#887 | 2 |
| C3×C4×Dic6 | 2 |
| C3×Q82 | 3 |
| #5722 | 3 |