Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
333 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 333 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 |
|---|---|---|
| 3. C2×C3×#216 | C2 | semidirect |
| 5. C3×#810 | C2 | semidirect |
| 7. #5050 | C3 | direct (N × H) |
| 25. C2×#216 | C2×C3 | semidirect |
| 29. #810 | C2×C3 | semidirect |
| 73. C22×C32 | Q16 | semidirect |
| 141. C22×C3 | #216 | semidirect |
| 142. C22×C3 | C3×Q16 | semidirect |
| 159. C32 | #451 | semidirect |
| 187. C22 | C3×#216 | semidirect |
| 195. C3 | #5050 | direct (N × H) |
| 196. C3 | C3×#451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic6 | 2 |
| C32×C22⋊Q8 | 2 |
| C2×C3×#216 | 2 |
| C3×#830 | 2 |
| C3×#810 | 2 |
| C3×#451 | 3 |
| #5050 | 3 |