Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
261 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 4. C3×Dic3⋊C8 | C2 | semidirect |
| 5. C3×C8×Dic3 | C2 | semidirect |
| 7. #4718 | C3 | direct (N × H) |
| 26. Dic3⋊C8 | C2×C3 | semidirect |
| 27. C8×Dic3 | C2×C3 | semidirect |
| 33. C2×C3×Dic3 | C8 | semidirect |
| 95. C2×Dic3 | C3×C8 | semidirect |
| 144. C32 | #431 | semidirect |
| 180. C3 | #4718 | direct (N × H) |
| 181. C3 | C3×#431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×Dic3 | 2 |
| C32×C22⋊C8 | 2 |
| C3×#830 | 2 |
| C3×Dic3⋊C8 | 2 |
| C3×C8×Dic3 | 2 |
| C3×#431 | 3 |
| #4718 | 3 |