Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
326 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 7. #10588743 | C3 | direct (N × H) |
| 35. C3×C9⋊C8 | Q8 | semidirect |
| 99. C9⋊C8 | C3×Q8 | semidirect |
| 152. C3×C9 | #501 | semidirect |
| 214. C9 | C3×#501 | semidirect |
| 240. C3 | #10588743 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#125 | 2 |
| C3×#63431 | 2 |
| C3×#63367 | 2 |
| C3×#63366 | 2 |
| C3×#63362 | 2 |
| C3×#5064 | 3 |
| #10588743 | 3 |