Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
506 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 89 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×Dic36 | C2 | semidirect |
| 3. #11720936 | C2 | semidirect |
| 4. C2×#88423 | C2 | semidirect |
| 5. #11720542 | C2 | semidirect |
| 6. C9×#821 | C2 | semidirect |
| 7. #11720268 | C2 | semidirect |
| 34. C2×Dic36 | D3 | semidirect |
| 117. #821 | D9 | semidirect |
| 246. C3×C9 | #452 | semidirect |
| 356. C9 | #5187 | semidirect |
| 404. C3 | #10588463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88639 | 2 |
| C2×C3×Dic36 | 2 |
| #11720936 | 2 |
| C2×#88423 | 2 |
| #11720542 | 2 |
| C9×#821 | 2 |
| #11720268 | 2 |
| #10590965 | 3 |
| #10588463 | 3 |