Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
775 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 775 conjugacy classes of subgroups — too many to draw. Only its 237 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. C24×3−1+2 | C2 | semidirect |
| 2. C23×AGL(1,ℤ/9) | C2 | semidirect |
| 3. C2×#611⋊C3 | C2 | direct (N × H) |
| 4. C22×3−1+2⋊C4 | C2 | semidirect |
| 6. C22×#611 | C3 | semidirect |
| 9. C23×3−1+2 | C22 | semidirect |
| 11. C22×AGL(1,ℤ/9) | C22 | semidirect |
| 12. #611⋊C3 | C22 | direct (N × H) |
| 13. C2×3−1+2⋊C4 | C22 | semidirect |
| 19. C24×C9 | C2×C3 | semidirect |
| 20. C23×D9 | C2×C3 | semidirect |
| 21. C2×#611 | C2×C3 | semidirect |
| 22. C22×Dic9 | C2×C3 | semidirect |
| 24. C22×3−1+2 | D4 | semidirect |
| 26. C22×3−1+2 | C23 | semidirect |
| 28. C2×AGL(1,ℤ/9) | C23 | semidirect |
| 29. 3−1+2⋊C4 | C23 | semidirect |
| 44. C23×C9 | C22×C3 | semidirect |
| 46. C22×D9 | C22×C3 | semidirect |
| 47. #611 | C22×C3 | semidirect |
| 48. C2×Dic9 | C22×C3 | semidirect |
| 50. C2×3−1+2 | C2×D4 | semidirect |
| 73. C22×C9 | C3×D4 | semidirect |
| 75. C22×C9 | C23×C3 | semidirect |
| 77. C2×D9 | C23×C3 | semidirect |
| 78. Dic9 | C23×C3 | semidirect |
| 80. 3−1+2 | C22×D4 | semidirect |
| 103. C2×C9 | C2×C3×D4 | semidirect |
| 107. C24 | AGL(1,ℤ/9) | semidirect |
| 126. C9 | C22×C3×D4 | semidirect |
| 131. C23 | C2×AGL(1,ℤ/9) | semidirect |
| 145. C22 | #611⋊C3 | direct (N × H) |
| 147. C22 | C22×AGL(1,ℤ/9) | semidirect |
| 153. C2 | C2×#611⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×3−1+2 | 2 |
| C23×AGL(1,ℤ/9) | 2 |
| C2×#611⋊C3 | 2 |
| C22×3−1+2⋊C4 | 2 |
| C22×C3×#67 | 3 |
| C22×#611 | 3 |