Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
776 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 208 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 | direct (N × H) |
| 3. C23×C32×C9 | C3 | semidirect |
| 4. C2×C32×C22⋊C9 | C3 | semidirect |
| 5. C2×(C3×A4)⋊C9 | C3 | direct (N × H) |
| 10. C22×C32×C9 | C2×C3 | semidirect |
| 11. C32×C22⋊C9 | C2×C3 | semidirect |
| 12. (C3×A4)⋊C9 | C2×C3 | direct (N × H) |
| 17. C2×C32×A4 | C9 | semidirect |
| 20. C23×C3×C9 | C32 | semidirect |
| 22. C2×C3×C22⋊C9 | C32 | semidirect |
| 27. C2×C32×C9 | A4 | semidirect |
| 34. C32×A4 | C2×C9 | semidirect |
| 41. C22×C3×C9 | C2×C32 | semidirect |
| 43. C3×C22⋊C9 | C2×C32 | semidirect |
| 46. C32×C9 | C2×A4 | semidirect |
| 55. C2×C3×A4 | C3×C9 | semidirect |
| 72. C2×C3×C9 | C3×A4 | semidirect |
| 88. C3×A4 | C2×C3×C9 | semidirect |
| 101. C3×C9 | C2×C3×A4 | semidirect |
| 102. C23×C3 | C32⋊C9 | semidirect |
| 135. C22×C3 | C2×C32⋊C9 | semidirect |
| 150. C23 | C3×C32⋊C9 | semidirect |
| 160. C2×C3 | (C3×A4)⋊C9 | direct (N × H) |
| 166. C22 | C2×C3×C32⋊C9 | semidirect |
| 168. C3 | C2×(C3×A4)⋊C9 | direct (N × H) |
| 174. C2 | C3×(C3×A4)⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×(C3×A4)⋊C9 | 2 |
| C2×C33×A4 | 3 |
| C23×C32×C9 | 3 |
| C2×C32×C22⋊C9 | 3 |
| C2×(C3×A4)⋊C9 | 3 |
| C2×C3×C32⋊C9 | 4 |