Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
340 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 43 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. C3×(C3×A4)⋊C9 | C2 | semidirect |
| 7. C22×C32×C9 | D3 | semidirect |
| 12. (C3×A4)⋊C9 | D3 | semidirect |
| 14. C3⋊(C3⋊S4) | C9 | semidirect |
| 30. C32×A4 | C2×C9 | semidirect |
| 35. C22×C3×C9 | C3⋊D3 | semidirect |
| 44. C32×C9 | S4 | semidirect |
| 79. C3×A4 | D3×C9 | semidirect |
| 99. C3×C9 | C3⋊S4 | semidirect |
| 122. C22×C3 | (C3⋊D3)⋊C9 | semidirect |
| 158. C22 | C3⋊((C3⋊D3)⋊C9) | semidirect |
| 164. C3 | (C3⋊S4)⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×(C3×A4)⋊C9 | 2 |
| C3×C3⋊(C3⋊S4) | 3 |
| C9×#638 | 3 |
| (C3⋊S4)⋊C9 | 3 |
| C3⋊((C3⋊D3)⋊C9) | 4 |