Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
412 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 190 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. C32×#125 | C2 | semidirect |
| 4. C3×#890 | C2 | semidirect |
| 5. C3×#887 | C2 | semidirect |
| 7. C3×#869 | C2 | semidirect |
| 9. #5698 | C3 | direct (N × H) |
| 27. C3×#125 | D3 | semidirect |
| 28. C3×#125 | C2×C3 | semidirect |
| 34. #890 | C2×C3 | semidirect |
| 35. #887 | C2×C3 | semidirect |
| 37. #869 | C2×C3 | semidirect |
| 89. #125 | C3×D3 | semidirect |
| 152. C32 | #541 | semidirect |
| 180. C3 | #5698 | direct (N × H) |
| 181. C3 | C3×#541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#125 | 2 |
| C3×#898 | 2 |
| C3×#897 | 2 |
| C3×#890 | 2 |
| C3×#887 | 2 |
| C3×#872 | 2 |
| C3×#869 | 2 |
| C3×#541 | 3 |
| #5698 | 3 |