Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
234 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 1. C2×C32×D8 | C2 | semidirect |
| 2. C2×C3×D24 | C2 | semidirect |
| 3. C3×#826 | C2 | direct (N × H) |
| 4. C2×C3×C3⋊C16 | C2 | semidirect |
| 6. C2×#826 | C3 | direct (N × H) |
| 10. C32×D8 | C22 | semidirect |
| 13. C3×D24 | C22 | semidirect |
| 14. C3×C3⋊C16 | C22 | semidirect |
| 17. C2×C3×D8 | D3 | semidirect |
| 18. C2×C3×D8 | C2×C3 | semidirect |
| 19. C2×D24 | C2×C3 | semidirect |
| 22. #826 | C2×C3 | direct (N × H) |
| 23. C2×C3⋊C16 | C2×C3 | semidirect |
| 45. C3×D8 | C2×D3 | semidirect |
| 46. C3×D8 | C22×C3 | semidirect |
| 51. D24 | C22×C3 | semidirect |
| 53. C3⋊C16 | C22×C3 | semidirect |
| 62. C2×D8 | C3×D3 | semidirect |
| 90. C2×C32 | D16 | semidirect |
| 98. D8 | C2×C3×D3 | semidirect |
| 120. C32 | C2×D16 | semidirect |
| 136. C2×C3 | #826 | direct (N × H) |
| 137. C2×C3 | C3×D16 | semidirect |
| 149. C3 | C2×#826 | direct (N × H) |
| 150. C3 | C2×C3×D16 | semidirect |
| 153. C2 | C3×#826 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D8 | 2 |
| C2×C3×D24 | 2 |
| C3×#826 | 2 |
| C2×C3×C3⋊C16 | 2 |
| C2×C3×D16 | 3 |
| C2×#826 | 3 |