Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
191 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 54 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×A4×C27 | C2 | semidirect |
| 3. C22×D3×C27 | C3 | semidirect |
| 5. D3×C22⋊C27 | C3 | semidirect |
| 8. C22×C3×C27 | C2×C3 | semidirect |
| 11. C3×C22⋊C27 | C2×C3 | semidirect |
| 15. A4×C27 | D3 | direct (N × H) |
| 28. D3×C27 | A4 | direct (N × H) |
| 41. C22×C27 | C3×D3 | semidirect |
| 43. C22⋊C27 | C3×D3 | semidirect |
| 50. C3×C27 | C2×A4 | semidirect |
| 53. D3×A4 | C27 | direct (N × H) |
| 72. C3×A4 | C2×C27 | semidirect |
| 90. C27 | D3×A4 | direct (N × H) |
| 92. C22×D3 | C3×C27 | semidirect |
| 107. C22×C3 | C2×C3×C27 | semidirect |
| 112. A4 | D3×C27 | direct (N × H) |
| 130. D3 | A4×C27 | direct (N × H) |
| 133. C22 | C3×D3×C27 | semidirect |
| 137. C3 | C2×A4×C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×C27 | 2 |
| D3×C9×A4 | 3 |
| C22×D3×C27 | 3 |
| C2×A4×C27 | 3 |
| D3×C22⋊C27 | 3 |
| C3×D3×C27 | 4 |