Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
302 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 47 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 | semidirect |
| 4. C22×(C3⋊D3)⋊C9 | C3 | semidirect |
| 5. (C3⋊D3)⋊(C22⋊C9) | C3 | semidirect |
| 9. C3×C9×A4 | D3 | semidirect |
| 10. C22×C32⋊C9 | C2×C3 | semidirect |
| 13. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 18. A4×C3⋊D3 | C9 | semidirect |
| 29. (C3⋊D3)⋊C9 | A4 | direct (N × H) |
| 38. C32×A4 | C2×C9 | semidirect |
| 41. C22×C3×C9 | C3×D3 | semidirect |
| 45. C3×C22⋊C9 | C3×D3 | semidirect |
| 56. C32⋊C9 | C2×A4 | semidirect |
| 57. C22×C3⋊D3 | C3×C9 | semidirect |
| 80. C22×C32 | C2×C3×C9 | semidirect |
| 120. C3×C9 | D3×A4 | semidirect |
| 132. C3⋊D3 | C9×A4 | semidirect |
| 157. A4 | (C3⋊D3)⋊C9 | direct (N × H) |
| 172. C32 | C2×C9×A4 | semidirect |
| 193. C22 | C3×(C3⋊D3)⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×C32⋊C9 | 2 |
| C3×A4×C3⋊D3 | 3 |
| D3×C9×A4 | 3 |
| C22×(C3⋊D3)⋊C9 | 3 |
| (C3⋊D3)⋊(C22⋊C9) | 3 |
| C3×(C3⋊D3)⋊C9 | 4 |