Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
462 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 113 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. C9×#869 | C2 | semidirect |
| 3. C3×C4×C9⋊C8 | C2 | semidirect |
| 4. #11720267 | C2 | semidirect |
| 23. C4×C9⋊C8 | D3 | semidirect |
| 68. #869 | D9 | semidirect |
| 152. C3×C9 | #486 | semidirect |
| 225. C9 | #4694 | semidirect |
| 257. C3 | #10588773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721711 | 2 |
| C9×#869 | 2 |
| C3×C4×C9⋊C8 | 2 |
| #11720267 | 2 |
| #10590281 | 3 |
| #10588773 | 3 |