Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
190 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. #131⋊C27 | C2 | direct (N × H) |
| 52. C2×#131 | C27 | semidirect |
| 78. #131 | C2×C27 | semidirect |
| 151. C2 | #131⋊C27 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41⋊C27 | 2 |
| #131⋊C27 | 2 |
| C2×C9×#131 | 3 |
| C2×C8×C27 | 4 |