Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
668 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 172 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. A4×C32⋊C9 | C2 | direct (N × H) |
| 3. C2×C3×C9×A4 | C3 | semidirect |
| 4. C23×C32⋊C9 | C3 | semidirect |
| 5. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 6. C2×(C3×A4)⋊C9 | C3 | semidirect |
| 9. C3×C9×A4 | C2×C3 | semidirect |
| 12. C22×C32⋊C9 | C2×C3 | semidirect |
| 13. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 14. (C3×A4)⋊C9 | C2×C3 | semidirect |
| 19. C2×C32×A4 | C9 | semidirect |
| 22. C23×C3×C9 | C32 | semidirect |
| 23. C2×C3×C22⋊C9 | C32 | semidirect |
| 31. C2×C32⋊C9 | A4 | direct (N × H) |
| 37. C32×A4 | C2×C9 | semidirect |
| 42. C22×C3×C9 | C2×C32 | semidirect |
| 43. C3×C22⋊C9 | C2×C32 | semidirect |
| 49. C32⋊C9 | C2×A4 | direct (N × H) |
| 52. C23×C32 | C3×C9 | semidirect |
| 58. C2×C3×A4 | C3×C9 | semidirect |
| 75. C2×C3×C9 | C3×A4 | semidirect |
| 86. C22×C32 | C2×C3×C9 | semidirect |
| 92. C3×A4 | C2×C3×C9 | semidirect |
| 107. C3×C9 | C2×C3×A4 | semidirect |
| 113. C2×A4 | C32⋊C9 | direct (N × H) |
| 131. C2×C32 | C9×A4 | semidirect |
| 150. A4 | C2×C32⋊C9 | direct (N × H) |
| 160. C32 | C2×C9×A4 | semidirect |
| 164. C23 | C3×C32⋊C9 | semidirect |
| 181. C22 | C2×C3×C32⋊C9 | semidirect |
| 190. C2 | A4×C32⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×C32⋊C9 | 2 |
| C2×C33×A4 | 3 |
| C2×C3×C9×A4 | 3 |
| C23×C32⋊C9 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×(C3×A4)⋊C9 | 3 |
| C2×C3×C32⋊C9 | 4 |