Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
150 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 45 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⋊D3)⋊C27 | C2 | semidirect |
| 2. C4×C32⋊C27 | C2 | semidirect |
| 11. C3×C4×C27 | D3 | semidirect |
| 12. C32⋊C27 | D4 | semidirect |
| 35. C3×C27 | D12 | semidirect |
| 36. C4⋊(C3⋊D3) | C27 | semidirect |
| 51. C2×C3⋊D3 | C2×C27 | semidirect |
| 57. C32×C4 | C2×C27 | semidirect |
| 96. C32 | D4×C27 | semidirect |
| 111. C4 | (C3⋊D3)⋊C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C3⋊D3)⋊C27 | 2 |
| C4×C32⋊C27 | 2 |
| C9×C4⋊(C3⋊D3) | 3 |
| D12×C27 | 3 |