Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
718 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 105 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. C32×C9×A4 | C2 | semidirect |
| 7. C22×C32×C9 | D3 | semidirect |
| 11. C3×C9×A4 | D3 | semidirect |
| 14. C3⋊(C3⋊S4) | C9 | direct (N × H) |
| 27. C32×A4 | C2×C9 | semidirect |
| 31. C22×C3×C9 | C3⋊D3 | semidirect |
| 35. C9×A4 | C3⋊D3 | semidirect |
| 41. C32×C9 | S4 | semidirect |
| 56. C22×C32 | D3×C9 | semidirect |
| 62. C3×A4 | D3×C9 | semidirect |
| 68. C22×C9 | C3⋊(C3⋊D3) | semidirect |
| 80. C3×C9 | C3⋊S4 | semidirect |
| 96. C22×C3 | C9×C3⋊D3 | semidirect |
| 100. A4 | C9×C3⋊D3 | semidirect |
| 108. C32 | C9×S4 | semidirect |
| 112. C9 | C3⋊(C3⋊S4) | direct (N × H) |
| 121. C22 | C9×C3⋊(C3⋊D3) | semidirect |
| 126. C3 | C9×C3⋊S4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×A4 | 2 |
| C3×C3⋊(C3⋊S4) | 3 |
| C9×C3⋊S4 | 3 |
| C9×#638 | 3 |
| C9×C3⋊(C3⋊D3) | 4 |