Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
270 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 142 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×#818 | C2 | semidirect |
| 5. C3×#817 | C2 | semidirect |
| 7. #5121 | C3 | direct (N × H) |
| 10. C32×M16 | C4 | semidirect |
| 27. #818 | C2×C3 | semidirect |
| 28. #817 | C2×C3 | semidirect |
| 38. C32×C8 | C2×C4 | semidirect |
| 46. C3×M16 | Dic3 | semidirect |
| 47. C3×M16 | C3×C4 | semidirect |
| 102. C3×C8 | C2×Dic3 | semidirect |
| 103. C3×C8 | C2×C3×C4 | semidirect |
| 110. M16 | C3×Dic3 | semidirect |
| 145. C32 | #428 | semidirect |
| 155. C8 | C2×C3×Dic3 | semidirect |
| 179. C3 | #5121 | direct (N × H) |
| 180. C3 | C3×#428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M16 | 2 |
| C3×#926 | 2 |
| C2×C3×C4⋊Dic3 | 2 |
| C3×#818 | 2 |
| C3×#817 | 2 |
| C3×#428 | 3 |
| #5121 | 3 |