Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
710 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 171 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. #11721866 | C2 | semidirect |
| 3. #11721854 | C2 | semidirect |
| 4. #11720585 | C2 | semidirect |
| 5. #11720581 | C2 | semidirect |
| 157. C3×C9 | #456 | semidirect |
| 218. C9 | #5246 | semidirect |
| 246. C3 | #10588925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×2−1+4 | 2 |
| #11721866 | 2 |
| #11721854 | 2 |
| #11720585 | 2 |
| #11720581 | 2 |
| #10592945 | 3 |
| #10588925 | 3 |