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×#3664 | C2 | semidirect |
| 3. #11720936 | C2 | semidirect |
| 4. C2×#88427 | C2 | semidirect |
| 5. #11720542 | C2 | semidirect |
| 6. C9×#816 | C2 | semidirect |
| 7. #11720266 | C2 | semidirect |
| 34. C2×#3664 | D3 | semidirect |
| 120. #816 | D9 | semidirect |
| 246. C3×C9 | #452 | semidirect |
| 356. C9 | #5173 | semidirect |
| 404. C3 | #10588488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88634 | 2 |
| C2×C3×#3664 | 2 |
| #11720936 | 2 |
| C2×#88427 | 2 |
| #11720542 | 2 |
| C9×#816 | 2 |
| #11720266 | 2 |
| #10590961 | 3 |
| #10588488 | 3 |