Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
178 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 62 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. C23×3−1+2 | C2 | semidirect |
| 2. C22×AGL(1,ℤ/9) | C2 | semidirect |
| 3. #611⋊C3 | C2 | direct (N × H) |
| 4. C2×3−1+2⋊C4 | C2 | semidirect |
| 6. C2×#611 | C3 | semidirect |
| 9. C22×3−1+2 | C22 | semidirect |
| 11. C2×AGL(1,ℤ/9) | C22 | semidirect |
| 12. 3−1+2⋊C4 | C22 | semidirect |
| 18. C23×C9 | C2×C3 | semidirect |
| 19. C22×D9 | C2×C3 | semidirect |
| 20. #611 | C2×C3 | semidirect |
| 21. C2×Dic9 | C2×C3 | semidirect |
| 23. C2×3−1+2 | D4 | semidirect |
| 39. C22×C9 | C22×C3 | semidirect |
| 41. C2×D9 | C22×C3 | semidirect |
| 42. Dic9 | C22×C3 | semidirect |
| 43. 3−1+2 | C2×D4 | semidirect |
| 60. C2×C9 | C3×D4 | semidirect |
| 78. C9 | C2×C3×D4 | semidirect |
| 80. C23 | AGL(1,ℤ/9) | semidirect |
| 95. C22 | C2×AGL(1,ℤ/9) | semidirect |
| 101. 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 |
|---|---|
| C23×3−1+2 | 2 |
| C22×AGL(1,ℤ/9) | 2 |
| #611⋊C3 | 2 |
| C2×3−1+2⋊C4 | 2 |
| C2×C3×#67 | 3 |
| C2×#611 | 3 |