Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
326 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 326 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 |
|---|---|---|
| 2. C3×#951 | C2 | semidirect |
| 3. C3×#909 | C2 | semidirect |
| 4. C3×#875 | C2 | semidirect |
| 5. C32×#104 | C2 | semidirect |
| 6. C3×#823 | C2 | semidirect |
| 7. C3×#805 | C2 | semidirect |
| 9. #4825 | C3 | direct (N × H) |
| 18. C2×C3×Dic6 | C22 | semidirect |
| 19. C32×M16 | C22 | semidirect |
| 20. C32×C42 | C22 | semidirect |
| 24. C3×#208 | C22 | semidirect |
| 32. #951 | C2×C3 | semidirect |
| 33. #909 | C2×C3 | semidirect |
| 34. #875 | C2×C3 | semidirect |
| 37. C3×#104 | D3 | semidirect |
| 38. C3×#104 | C2×C3 | semidirect |
| 40. #823 | C2×C3 | semidirect |
| 41. #805 | C2×C3 | semidirect |
| 83. C2×Dic6 | C22×C3 | semidirect |
| 90. C3×M16 | C2×D3 | semidirect |
| 91. C3×M16 | C22×C3 | semidirect |
| 94. C3×C42 | C2×D3 | semidirect |
| 95. C3×C42 | C22×C3 | semidirect |
| 99. #208 | C22×C3 | semidirect |
| 119. #104 | C3×D3 | semidirect |
| 191. M16 | C2×C3×D3 | semidirect |
| 193. C42 | C2×C3×D3 | semidirect |
| 224. C32 | #455 | semidirect |
| 273. C3 | #4825 | direct (N × H) |
| 274. C3 | C3×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1009 | 2 |
| C3×#951 | 2 |
| C3×#909 | 2 |
| C3×#875 | 2 |
| C32×#104 | 2 |
| C3×#823 | 2 |
| C3×#805 | 2 |
| C3×#455 | 3 |
| #4825 | 3 |