Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
558 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 558 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. C3×C9×#123 | C2 | semidirect |
| 3. C9×#929 | C2 | semidirect |
| 4. C9×#834 | C2 | semidirect |
| 5. C9×#806 | C2 | semidirect |
| 9. C22×C3×C4×C9 | C22 | semidirect |
| 17. C3×C9×C22⋊C4 | C22 | semidirect |
| 18. C9×#217 | C22 | semidirect |
| 29. C9×#123 | D3 | semidirect |
| 51. #5053 | C9 | direct (N × H) |
| 73. C22×C4×C9 | C2×D3 | semidirect |
| 82. C9×C22⋊C4 | C2×D3 | semidirect |
| 100. C3×#123 | C2×C9 | semidirect |
| 102. #929 | C2×C9 | semidirect |
| 105. #834 | C2×C9 | semidirect |
| 106. #806 | C2×C9 | semidirect |
| 165. C22×C3×C4 | C22×C9 | semidirect |
| 182. C3×C22⋊C4 | C22×C9 | semidirect |
| 184. #217 | C22×C9 | semidirect |
| 223. #123 | D3×C9 | semidirect |
| 226. C3×C9 | #458 | semidirect |
| 290. C22×C4 | C2×D3×C9 | semidirect |
| 296. C22⋊C4 | C2×D3×C9 | semidirect |
| 333. C9 | #5053 | direct (N × H) |
| 380. 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 |
| C3×C9×#123 | 2 |
| C9×#929 | 2 |
| C9×#834 | 2 |
| C9×#806 | 2 |
| C3×#5053 | 3 |
| C9×#458 | 3 |