Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
474 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 231 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×C3×C27⋊C3 | C2 | semidirect |
| 2. C2×D3×C27⋊C3 | C2 | direct (N × H) |
| 5. C22×D3×C27 | C3 | semidirect |
| 6. C2×C3×C27⋊C3 | C22 | semidirect |
| 7. D3×C27⋊C3 | C22 | direct (N × H) |
| 13. C22×C27⋊C3 | D3 | direct (N × H) |
| 14. C22×C3×C27 | C2×C3 | semidirect |
| 15. C2×D3×C27 | C2×C3 | semidirect |
| 16. C3×C27⋊C3 | C23 | semidirect |
| 27. C2×C27⋊C3 | C2×D3 | direct (N × H) |
| 28. C2×C3×C27 | C22×C3 | semidirect |
| 29. D3×C27 | C22×C3 | semidirect |
| 43. C22×C27 | C3×D3 | semidirect |
| 47. C27⋊C3 | C22×D3 | direct (N × H) |
| 48. C3×C27 | C23×C3 | semidirect |
| 67. C2×C27 | C2×C3×D3 | semidirect |
| 90. C27 | C22×C3×D3 | semidirect |
| 93. C22×D3 | C27⋊C3 | direct (N × H) |
| 113. C22×C3 | C2×C27⋊C3 | semidirect |
| 115. C2×D3 | C2×C27⋊C3 | direct (N × H) |
| 131. C2×C3 | C22×C27⋊C3 | semidirect |
| 133. D3 | C22×C27⋊C3 | direct (N × H) |
| 135. C22 | D3×C27⋊C3 | direct (N × H) |
| 139. C3 | C23×C27⋊C3 | semidirect |
| 142. C2 | C2×D3×C27⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C27⋊C3 | 2 |
| C2×D3×C27⋊C3 | 2 |
| C22×C3×D3×C9 | 3 |
| C23×C27⋊C3 | 3 |
| C22×D3×C27 | 3 |