Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
251 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 251 conjugacy classes of subgroups — too many to draw. Only its 72 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. C32×C22⋊C27 | C2 | semidirect |
| 4. D3×C22⋊C27 | C3 | direct (N × H) |
| 11. C3×C22⋊C27 | D3 | direct (N × H) |
| 12. C3×C22⋊C27 | C2×C3 | semidirect |
| 40. C22⋊C27 | C3×D3 | direct (N × H) |
| 47. C22×C3×D3 | C27 | semidirect |
| 71. C22×C32 | C2×C27 | semidirect |
| 97. C22×D3 | C3×C27 | semidirect |
| 107. C3×D3 | C22⋊C27 | direct (N × H) |
| 123. C22×C3 | D3×C27 | semidirect |
| 124. C22×C3 | C2×C3×C27 | semidirect |
| 130. C32 | C2×C22⋊C27 | semidirect |
| 148. D3 | C3×C22⋊C27 | direct (N × H) |
| 151. C22 | C3×D3×C27 | semidirect |
| 154. C3 | D3×C22⋊C27 | direct (N × H) |
| 155. C3 | C2×C3×C22⋊C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C22⋊C27 | 2 |
| C22×C3×D3×C9 | 3 |
| C2×C3×C22⋊C27 | 3 |
| D3×C22⋊C27 | 3 |
| C3×D3×C27 | 4 |