Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
532 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 117 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×#935 | C2 | semidirect |
| 3. C9×#886 | C2 | semidirect |
| 4. C3×C9×#99 | C2 | semidirect |
| 5. C9×#806 | C2 | semidirect |
| 11. C22×C9×Dic3 | C22 | semidirect |
| 15. C3×C9×C22⋊C4 | C22 | semidirect |
| 17. C9×#217 | C22 | semidirect |
| 31. C9×#99 | D3 | semidirect |
| 51. #4742 | C9 | direct (N × H) |
| 79. C9×C22⋊C4 | C2×D3 | semidirect |
| 97. #935 | C2×C9 | semidirect |
| 98. #886 | C2×C9 | semidirect |
| 101. C3×#99 | C2×C9 | semidirect |
| 103. #806 | C2×C9 | semidirect |
| 162. C22×Dic3 | C22×C9 | semidirect |
| 172. C3×C22⋊C4 | C22×C9 | semidirect |
| 175. #217 | C22×C9 | semidirect |
| 216. #99 | D3×C9 | semidirect |
| 217. C3×C9 | #458 | semidirect |
| 285. C22⋊C4 | C2×D3×C9 | semidirect |
| 321. C9 | #4742 | direct (N × H) |
| 368. C3 | C9×#458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1004 | 2 |
| C9×#935 | 2 |
| C9×#886 | 2 |
| C3×C9×#99 | 2 |
| C9×#806 | 2 |
| C3×#4742 | 3 |
| C9×#458 | 3 |