Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
191 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 19. #5403 | C9 | direct (N × H) |
| 122. C9 | #5403 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#984 | 2 |
| C9×#131⋊C3 | 2 |
| C3×#5403 | 3 |
| C9×#473 | 3 |
| C9×Dic12 | 4 |