Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
290 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 99 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×C32⋊C27 | C2 | semidirect |
| 2. C2×(C3⋊D3)⋊C27 | C2 | direct (N × H) |
| 5. C2×C32⋊C27 | C22 | semidirect |
| 6. (C3⋊D3)⋊C27 | C22 | direct (N × H) |
| 10. C22×C3×C27 | D3 | semidirect |
| 12. C32⋊C27 | C23 | semidirect |
| 20. C2×C3×C27 | C2×D3 | semidirect |
| 35. C3×C27 | C22×D3 | semidirect |
| 36. C22×C3⋊D3 | C27 | semidirect |
| 54. C22×C32 | C2×C27 | semidirect |
| 56. C2×C3⋊D3 | C2×C27 | semidirect |
| 76. C2×C32 | C22×C27 | semidirect |
| 78. C3⋊D3 | C22×C27 | semidirect |
| 96. C32 | C23×C27 | semidirect |
| 111. C22 | (C3⋊D3)⋊C27 | direct (N × H) |
| 118. C2 | C2×(C3⋊D3)⋊C27 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32⋊C27 | 2 |
| C2×(C3⋊D3)⋊C27 | 2 |
| C22×C9×C3⋊D3 | 3 |
| C22×D3×C27 | 3 |