Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
160 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 160 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. (C22⋊C9)⋊C27 | C2 | direct (N × H) |
| 38. C2×C22⋊C9 | C27 | semidirect |
| 58. C22⋊C9 | C2×C27 | semidirect |
| 92. C23 | C9⋊C27 | semidirect |
| 104. C22 | C2×C9⋊C27 | semidirect |
| 110. C2 | (C22⋊C9)⋊C27 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C22⋊C9)⋊C27 | 2 |
| C23×C3×C27 | 3 |
| C2×C9×C22⋊C9 | 3 |
| C2×C3×C22⋊C27 | 3 |
| C2×C9⋊C27 | 4 |