Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
272 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 272 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 |
|---|---|---|
| 2. C9×A4⋊Q8 | C2 | semidirect |
| 3. C9×A4⋊C8 | C2 | semidirect |
| 26. #5414 | C9 | direct (N × H) |
| 49. C9×A4 | SD16 | semidirect |
| 55. A4⋊Q8 | C2×C9 | semidirect |
| 59. A4⋊C8 | C2×C9 | semidirect |
| 124. C22×C9 | #214 | semidirect |
| 199. A4 | C9×SD16 | semidirect |
| 209. C9 | #5414 | direct (N × H) |
| 244. C22 | C9×#214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C9×A4 | 2 |
| C9×A4⋊Q8 | 2 |
| C9×A4⋊C8 | 2 |
| C3×#5414 | 3 |
| C9×#450 | 3 |
| C9×#214 | 4 |