Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
377 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 377 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
| 3. C22×C3×D3×C9 | C3 | semidirect |
| 4. C3×D3×C22⋊C9 | C3 | semidirect |
| 8. C22×C32×C9 | C2×C3 | semidirect |
| 11. C32×C22⋊C9 | C2×C3 | semidirect |
| 15. (C3×A4)⋊C9 | D3 | direct (N × H) |
| 21. C3×D3×A4 | C9 | semidirect |
| 30. C3×D3×C9 | A4 | semidirect |
| 41. C32×A4 | C2×C9 | semidirect |
| 48. C22×C3×C9 | C3×D3 | semidirect |
| 54. C3×C22⋊C9 | C3×D3 | semidirect |
| 57. C32×C9 | C2×A4 | semidirect |
| 113. C3×A4 | D3×C9 | semidirect |
| 136. C3×C9 | D3×A4 | semidirect |
| 140. C22×D3 | C32⋊C9 | semidirect |
| 175. C22×C3 | C2×C32⋊C9 | semidirect |
| 220. D3 | (C3×A4)⋊C9 | direct (N × H) |
| 223. C22 | D3×C32⋊C9 | semidirect |
| 229. C3 | C2×(C3×A4)⋊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 |
| C32×D3×A4 | 3 |
| C22×C3×D3×C9 | 3 |
| C3×D3×C22⋊C9 | 3 |
| C2×(C3×A4)⋊C9 | 3 |
| D3×C32⋊C9 | 4 |