Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
334 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 182 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 |
|---|---|---|
| 2. C3×Dic3×C27 | C2 | direct (N × H) |
| 5. C2×Dic3×C27 | C3 | direct (N × H) |
| 6. C2×C32×C27 | C4 | semidirect |
| 15. Dic3×C27 | C2×C3 | direct (N × H) |
| 16. C32×C27 | C2×C4 | semidirect |
| 28. C2×C3×C27 | Dic3 | direct (N × H) |
| 29. C2×C3×C27 | C3×C4 | semidirect |
| 49. C3×C27 | C2×Dic3 | direct (N × H) |
| 50. C3×C27 | C2×C3×C4 | semidirect |
| 52. C2×C3×Dic3 | C27 | direct (N × H) |
| 72. C2×C27 | C3×Dic3 | direct (N × H) |
| 80. C3×Dic3 | C2×C27 | direct (N × H) |
| 96. C27 | C2×C3×Dic3 | direct (N × H) |
| 99. C2×Dic3 | C3×C27 | direct (N × H) |
| 104. C2×C32 | C4×C27 | semidirect |
| 125. Dic3 | C2×C3×C27 | direct (N × H) |
| 128. C32 | C2×C4×C27 | semidirect |
| 140. C2×C3 | Dic3×C27 | direct (N × H) |
| 141. C2×C3 | C3×C4×C27 | semidirect |
| 150. C3 | C2×Dic3×C27 | direct (N × H) |
| 151. C3 | C2×C3×C4×C27 | semidirect |
| 153. C2 | C3×Dic3×C27 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C27 | 2 |
| C3×Dic3×C27 | 2 |
| C2×C3×C9×Dic3 | 3 |
| C2×C3×C4×C27 | 3 |
| C2×Dic3×C27 | 3 |