Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
514 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 514 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 |
|---|---|---|
| 1. C9×#1007 | C2 | semidirect |
| 2. C3×C9×#124 | C2 | semidirect |
| 3. C9×#932 | C2 | semidirect |
| 4. C9×#836 | C2 | semidirect |
| 5. C9×#805 | C2 | semidirect |
| 27. C9×#124 | D3 | semidirect |
| 45. #5062 | C9 | direct (N × H) |
| 81. #1007 | C2×C9 | semidirect |
| 84. C3×#124 | C2×C9 | semidirect |
| 86. #932 | C2×C9 | semidirect |
| 89. #836 | C2×C9 | semidirect |
| 90. #805 | C2×C9 | semidirect |
| 180. #124 | D3×C9 | semidirect |
| 183. C3×C9 | #454 | semidirect |
| 264. C9 | #5062 | direct (N × H) |
| 299. C3 | C9×#454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1007 | 2 |
| C3×C9×#124 | 2 |
| C9×#932 | 2 |
| C9×#836 | 2 |
| C9×#805 | 2 |
| C3×#5062 | 3 |
| C9×#454 | 3 |