Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
472 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 110 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⋊D3×C27⋊C3 | C2 | semidirect |
| 2. C3×D3×C27⋊C3 | C2 | semidirect |
| 5. D32×C27 | C3 | semidirect |
| 6. C32×C27⋊C3 | C22 | semidirect |
| 10. C3⋊D3×C27 | C2×C3 | semidirect |
| 15. D3×C27⋊C3 | D3 | direct (N × H) |
| 16. C3×D3×C27 | C2×C3 | semidirect |
| 29. C3×C27⋊C3 | C2×D3 | semidirect |
| 30. C32×C27 | C22×C3 | semidirect |
| 52. D3×C27 | C3×D3 | semidirect |
| 77. C27⋊C3 | D32 | direct (N × H) |
| 81. C3×C27 | C2×C3×D3 | semidirect |
| 113. D32 | C27⋊C3 | direct (N × H) |
| 145. C27 | C3×D32 | semidirect |
| 152. C3⋊D3 | C2×C27⋊C3 | semidirect |
| 160. C3×D3 | C2×C27⋊C3 | semidirect |
| 184. C32 | C22×C27⋊C3 | semidirect |
| 202. D3 | D3×C27⋊C3 | direct (N × H) |
| 210. C3 | C2×D3×C27⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×C27⋊C3 | 2 |
| C3×D3×C27⋊C3 | 2 |
| C3×D32×C9 | 3 |
| C2×D3×C27⋊C3 | 3 |
| D32×C27 | 3 |