Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
246 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 86 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. #5182 | C3 | direct (N × H) |
| 92. C3×Dic3 | Q16 | semidirect |
| 176. Dic3 | C3×Q16 | semidirect |
| 177. C32 | #462 | semidirect |
| 212. C3 | #5182 | direct (N × H) |
| 213. C3 | C3×#462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q16 | 2 |
| C3×Q8×Dic3 | 2 |
| C3×#944 | 2 |
| C2×C3×#216 | 2 |
| C3×#835 | 2 |
| C3×#816 | 2 |
| C3×Dic3⋊C8 | 2 |
| C3×#462 | 3 |
| #5182 | 3 |