Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
387 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 119 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. #63716 | C2 | semidirect |
| 2. #63710 | C2 | semidirect |
| 3. C9×AGL(1,ℤ/8) | C2 | semidirect |
| 4. #63513 | C2 | semidirect |
| 5. C2×#3672 | C2 | semidirect |
| 6. #63477 | C2 | semidirect |
| 7. SD16×D9 | C2 | semidirect |
| 8. #63474 | C2 | semidirect |
| 9. #63473 | C2 | semidirect |
| 10. #63471 | C2 | semidirect |
| 11. #63469 | C2 | semidirect |
| 13. C9×#41 | C22 | semidirect |
| 16. Q8×D9 | C22 | semidirect |
| 20. #3699 | C22 | semidirect |
| 27. C2×Dic18 | C22 | semidirect |
| 28. C9×SD16 | C22 | semidirect |
| 29. C9×D8 | C22 | semidirect |
| 30. C9×M16 | C22 | semidirect |
| 31. #3675 | C22 | semidirect |
| 32. #3674 | C22 | semidirect |
| 33. #3673 | C22 | semidirect |
| 34. #3672 | C22 | semidirect |
| 35. #3672 | C22 | semidirect |
| 36. #3672 | C22 | semidirect |
| 37. C2×C9⋊C8 | C22 | semidirect |
| 38. #3664 | C22 | semidirect |
| 39. #3663 | C22 | semidirect |
| 40. C8×D9 | C22 | semidirect |
| 41. Dic36 | C22 | semidirect |
| 131. AGL(1,ℤ/8) | D9 | semidirect |
| 180. #41 | C2×D9 | semidirect |
| 195. SD16 | C2×D9 | semidirect |
| 197. D8 | C2×D9 | semidirect |
| 199. M16 | C2×D9 | semidirect |
| 215. C9 | #577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63716 | 2 |
| #63710 | 2 |
| C9×AGL(1,ℤ/8) | 2 |
| #63513 | 2 |
| C2×#3672 | 2 |
| #63477 | 2 |
| SD16×D9 | 2 |
| #63474 | 2 |
| #63473 | 2 |
| #63471 | 2 |
| #63469 | 2 |
| #5775 | 3 |