Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
234 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 25. #5416 | C9 | direct (N × H) |
| 47. C9×A4 | Q16 | semidirect |
| 111. C22×C9 | #216 | semidirect |
| 173. A4 | C9×Q16 | semidirect |
| 187. C9 | #5416 | direct (N × H) |
| 210. C22 | C9×#216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C9×A4 | 2 |
| C9×A4⋊Q8 | 2 |
| C9×A4⋊C8 | 2 |
| C3×#5416 | 3 |
| C9×#451 | 3 |
| C9×#216 | 4 |