Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
402 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
| 4. #568⋊C9 | C3 | direct (N × H) |
| 15. #131⋊C9 | C2×C3 | semidirect |
| 19. C3×#568 | C9 | semidirect |
| 45. C3×#131 | C2×C9 | semidirect |
| 68. #568 | C3×C9 | semidirect |
| 110. #131 | C2×C3×C9 | semidirect |
| 209. C3 | #568⋊C9 | direct (N × H) |
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 |
| C32×#568 | 3 |
| #568⋊C9 | 3 |
| C3×C9×M16 | 4 |