Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
196 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 64 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×A4)⋊C27 | C2 | direct (N × H) |
| 3. C23×C3×C27 | C3 | semidirect |
| 4. C2×C3×C22⋊C27 | C3 | semidirect |
| 9. C22×C3×C27 | C2×C3 | semidirect |
| 10. C3×C22⋊C27 | C2×C3 | semidirect |
| 23. C2×C3×C27 | A4 | semidirect |
| 37. C3×C27 | C2×A4 | semidirect |
| 41. C2×C3×A4 | C27 | semidirect |
| 61. C3×A4 | C2×C27 | semidirect |
| 110. C23 | C32⋊C27 | semidirect |
| 123. C22 | C2×C32⋊C27 | semidirect |
| 130. C2 | (C3×A4)⋊C27 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C3×A4)⋊C27 | 2 |
| C2×C3×C9×A4 | 3 |
| C23×C3×C27 | 3 |
| C2×C3×C22⋊C27 | 3 |
| C2×C32⋊C27 | 4 |