Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
634 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 177 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×C9×Dic3⋊C4 | C2 | semidirect |
| 3. C3×C9×#95 | C2 | semidirect |
| 17. C9×#95 | D3 | semidirect |
| 29. #4676 | C9 | direct (N × H) |
| 52. C2×Dic3⋊C4 | C2×C9 | semidirect |
| 54. C3×#95 | C2×C9 | semidirect |
| 118. #95 | D3×C9 | semidirect |
| 119. C3×C9 | #396 | semidirect |
| 182. C9 | #4676 | direct (N × H) |
| 213. C3 | C9×#396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×(C2×D3)⋊C4 | 2 |
| C2×C9×Dic3⋊C4 | 2 |
| C3×C9×#95 | 2 |
| C3×#4676 | 3 |
| C9×#396 | 3 |