Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
194 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 81 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×C3×C9 | C2 | semidirect |
| 2. C22×D3×C9 | C2 | semidirect |
| 3. C9×#67 | C2 | direct (N × H) |
| 4. C2×C9×Dic3 | C2 | semidirect |
| 9. C22×C3×C9 | C22 | semidirect |
| 11. C2×D3×C9 | C22 | semidirect |
| 12. C9×Dic3 | C22 | semidirect |
| 19. C23×C9 | D3 | semidirect |
| 23. C2×C3×C9 | D4 | semidirect |
| 27. C2×#67 | C9 | direct (N × H) |
| 41. C22×C9 | C2×D3 | semidirect |
| 43. C3×C9 | C2×D4 | semidirect |
| 46. C23×C3 | C2×C9 | semidirect |
| 48. C22×D3 | C2×C9 | semidirect |
| 51. #67 | C2×C9 | direct (N × H) |
| 52. C2×Dic3 | C2×C9 | semidirect |
| 62. C2×C9 | #67 | direct (N × H) |
| 73. C22×C3 | C22×C9 | semidirect |
| 77. C2×D3 | C22×C9 | semidirect |
| 79. Dic3 | C22×C9 | semidirect |
| 82. C9 | C2×#67 | direct (N × H) |
| 84. C23 | D3×C9 | semidirect |
| 93. C2×C3 | D4×C9 | semidirect |
| 102. C22 | C2×D3×C9 | semidirect |
| 105. C3 | C2×D4×C9 | semidirect |
| 109. C2 | C9×#67 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C9 | 2 |
| C22×D3×C9 | 2 |
| C9×#67 | 2 |
| C2×C9×Dic3 | 2 |
| C2×C3×#67 | 3 |
| C2×D4×C9 | 3 |