Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
214 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 49 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. C2×C3×C22⋊C27 | C2 | semidirect |
| 2. D3×C22⋊C27 | C2 | direct (N × H) |
| 6. C3×C22⋊C27 | C22 | semidirect |
| 14. C2×C22⋊C27 | D3 | direct (N × H) |
| 30. C22⋊C27 | C2×D3 | direct (N × H) |
| 52. C23×D3 | C27 | semidirect |
| 82. C23×C3 | C2×C27 | semidirect |
| 87. C22×D3 | C2×C27 | semidirect |
| 115. C22×C3 | C22×C27 | semidirect |
| 122. C2×D3 | C22⋊C27 | direct (N × H) |
| 130. C23 | D3×C27 | semidirect |
| 140. C2×C3 | C2×C22⋊C27 | semidirect |
| 143. D3 | C2×C22⋊C27 | direct (N × H) |
| 152. C22 | C2×D3×C27 | semidirect |
| 154. C3 | C22×C22⋊C27 | semidirect |
| 160. C2 | D3×C22⋊C27 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊C27 | 2 |
| D3×C22⋊C27 | 2 |
| C23×D3×C9 | 3 |
| C22×C22⋊C27 | 3 |
| C2×D3×C27 | 4 |