Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
245 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 245 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. C2×C3×#216 | C2 | semidirect |
| 4. C3×#887 | C2 | semidirect |
| 5. C32×#103 | C2 | semidirect |
| 6. C3×Dic3⋊C8 | C2 | semidirect |
| 9. #4798 | C3 | direct (N × H) |
| 28. C2×#216 | C2×C3 | semidirect |
| 30. #887 | C2×C3 | semidirect |
| 33. C3×#103 | D3 | semidirect |
| 34. C3×#103 | C2×C3 | semidirect |
| 36. Dic3⋊C8 | C2×C3 | semidirect |
| 99. #103 | C3×D3 | semidirect |
| 181. C32 | #464 | semidirect |
| 220. C3 | #4798 | direct (N × H) |
| 221. C3 | C3×#464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#947 | 2 |
| C2×C3×#216 | 2 |
| C2×C3×#204 | 2 |
| C3×#887 | 2 |
| C32×#103 | 2 |
| C3×Dic3⋊C8 | 2 |
| C3×#809 | 2 |
| C3×#464 | 3 |
| #4798 | 3 |