Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
243 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 243 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 |
|---|---|---|
| 1. C2×C3×Dic12 | C2 | semidirect |
| 4. C3×C4×Dic6 | C2 | semidirect |
| 5. C32×C4⋊C8 | C2 | semidirect |
| 7. C3×#816 | C2 | semidirect |
| 9. #4845 | C3 | direct (N × H) |
| 27. C2×Dic12 | C2×C3 | semidirect |
| 30. C4×Dic6 | C2×C3 | semidirect |
| 32. C3×C4⋊C8 | D3 | semidirect |
| 33. C3×C4⋊C8 | C2×C3 | semidirect |
| 37. #816 | C2×C3 | semidirect |
| 98. C4⋊C8 | C3×D3 | semidirect |
| 180. C32 | #464 | semidirect |
| 219. C3 | #4845 | direct (N × H) |
| 220. C3 | C3×#464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| C2×C3×#204 | 2 |
| C3×#875 | 2 |
| C3×C4×Dic6 | 2 |
| C32×C4⋊C8 | 2 |
| C3×#821 | 2 |
| C3×#816 | 2 |
| C3×#464 | 3 |
| #4845 | 3 |