Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
211 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 211 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 |
|---|---|---|
| 19. #5398 | C9 | direct (N × H) |
| 34. C9×A4 | Q16 | semidirect |
| 79. C22×C9 | Dic12 | semidirect |
| 124. A4 | C9×Q16 | semidirect |
| 134. C9 | #5398 | direct (N × H) |
| 151. C22 | C9×Dic12 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×A4⋊Q8 | 2 |
| C8×C9×A4 | 2 |
| C3×#5398 | 3 |
| C9×#467 | 3 |
| C9×Dic12 | 4 |