Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
341 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 110 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×D3×C8 | C2 | semidirect |
| 3. C3×#892 | C2 | semidirect |
| 4. C32×#102 | C2 | semidirect |
| 5. C3×#832 | C2 | semidirect |
| 6. C3×#816 | C2 | semidirect |
| 7. C3×#810 | C2 | semidirect |
| 9. #4772 | C3 | direct (N × H) |
| 14. C3×#237 | C4 | semidirect |
| 28. C2×D3×C8 | C2×C3 | semidirect |
| 29. #892 | C2×C3 | semidirect |
| 34. C3×#102 | D3 | semidirect |
| 35. C3×#102 | C2×C3 | semidirect |
| 36. #832 | C2×C3 | semidirect |
| 37. #816 | C2×C3 | semidirect |
| 38. #810 | C2×C3 | semidirect |
| 69. #237 | C3×C4 | semidirect |
| 107. #102 | C3×D3 | semidirect |
| 200. C32 | #416 | semidirect |
| 246. C3 | #4772 | direct (N × H) |
| 247. C3 | C3×#416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#237 | 2 |
| C2×C3×D3×C8 | 2 |
| C3×#892 | 2 |
| C32×#102 | 2 |
| C3×#832 | 2 |
| C3×#816 | 2 |
| C3×#810 | 2 |
| C3×#416 | 3 |
| #4772 | 3 |