Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
200 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 75 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×M32 | C2 | semidirect |
| 3. C9×#817 | C2 | semidirect |
| 9. C9×Dic12 | C4 | semidirect |
| 10. C9×D24 | C4 | semidirect |
| 18. C9×M32 | D3 | semidirect |
| 29. #4518 | C9 | direct (N × H) |
| 55. C3×M32 | C2×C9 | semidirect |
| 58. #817 | C2×C9 | semidirect |
| 92. Dic12 | C4×C9 | semidirect |
| 93. D24 | C4×C9 | semidirect |
| 114. M32 | D3×C9 | semidirect |
| 116. C3×C9 | #360 | semidirect |
| 168. C9 | #4518 | direct (N × H) |
| 192. C3 | C9×#360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#904 | 2 |
| C3×C9×M32 | 2 |
| C9×#817 | 2 |
| C3×#4518 | 3 |
| C9×#360 | 3 |