Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
226 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×C3×C9×C16 | C2 | semidirect |
| 3. C9×#818 | C2 | semidirect |
| 10. C9×D24 | C4 | semidirect |
| 17. C2×C9×C16 | D3 | semidirect |
| 27. #4509 | C9 | direct (N × H) |
| 52. C2×C3×C16 | C2×C9 | semidirect |
| 55. #818 | C2×C9 | semidirect |
| 88. D24 | C4×C9 | semidirect |
| 110. C2×C16 | D3×C9 | semidirect |
| 112. C3×C9 | #357 | semidirect |
| 166. C9 | #4509 | direct (N × H) |
| 193. C3 | C9×#357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D24 | 2 |
| C2×C3×C9×C16 | 2 |
| C9×#818 | 2 |
| C3×#4509 | 3 |
| C9×#357 | 3 |