Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
305 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 305 conjugacy classes of subgroups — too many to draw. Only its 69 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. C3⋊(#131⋊C9) | C2 | semidirect |
| 21. #5819 | C9 | semidirect |
| 53. #948 | C2×C9 | semidirect |
| 254. C3 | #568⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41⋊C9 | 2 |
| C3⋊(#131⋊C9) | 2 |
| C3×#5819 | 3 |
| #568⋊C9 | 3 |
| C9×#208 | 4 |