Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
334 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 126 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. C22×C32×C27 | C2 | semidirect |
| 2. C2×C3×D3×C27 | C2 | semidirect |
| 3. C3×Dic3×C27 | C2 | semidirect |
| 6. #67×C27 | C3 | direct (N × H) |
| 16. C22×C3×C27 | D3 | semidirect |
| 17. C22×C3×C27 | C2×C3 | semidirect |
| 18. C2×D3×C27 | C2×C3 | semidirect |
| 20. Dic3×C27 | C2×C3 | semidirect |
| 21. C32×C27 | D4 | semidirect |
| 57. C22×C27 | C3×D3 | semidirect |
| 62. C3×C27 | #67 | direct (N × H) |
| 63. C3×C27 | C3×D4 | semidirect |
| 65. C3×#67 | C27 | direct (N × H) |
| 95. C22×C32 | C2×C27 | semidirect |
| 98. C2×C3×D3 | C2×C27 | semidirect |
| 101. C3×Dic3 | C2×C27 | semidirect |
| 119. C27 | C3×#67 | direct (N × H) |
| 122. #67 | C3×C27 | direct (N × H) |
| 150. C22×C3 | D3×C27 | semidirect |
| 151. C22×C3 | C2×C3×C27 | semidirect |
| 153. C2×D3 | C2×C3×C27 | semidirect |
| 156. Dic3 | C2×C3×C27 | semidirect |
| 159. C32 | D4×C27 | semidirect |
| 181. C22 | C3×D3×C27 | semidirect |
| 185. C3 | #67×C27 | direct (N × H) |
| 186. C3 | C3×D4×C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C27 | 2 |
| C2×C3×D3×C27 | 2 |
| C3×Dic3×C27 | 2 |
| C3×C9×#67 | 3 |
| C3×D4×C27 | 3 |
| #67×C27 | 3 |