Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
237 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 237 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 |
|---|---|---|
| 9. #4795 | C3 | direct (N × H) |
| 91. C3×Dic3 | Q16 | semidirect |
| 173. Dic3 | C3×Q16 | semidirect |
| 174. C32 | #462 | semidirect |
| 209. C3 | #4795 | direct (N × H) |
| 210. C3 | C3×#462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#944 | 2 |
| C2×C3×#216 | 2 |
| C2×C3×Dic12 | 2 |
| C3×#887 | 2 |
| C32×#103 | 2 |
| C3×Dic3⋊C8 | 2 |
| C3×#810 | 2 |
| C3×#462 | 3 |
| #4795 | 3 |