Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
516 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 516 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×#88547 | C2 | semidirect |
| 3. C9×#946 | C2 | semidirect |
| 4. C2×C3×#3675 | C2 | semidirect |
| 5. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 6. #11720269 | C2 | semidirect |
| 7. #11720266 | C2 | semidirect |
| 34. C2×#3675 | D3 | semidirect |
| 112. #946 | D9 | semidirect |
| 247. C3×C9 | #452 | semidirect |
| 355. C9 | #5173 | semidirect |
| 402. C3 | #10588730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88641 | 2 |
| C2×#88547 | 2 |
| C9×#946 | 2 |
| C2×C3×#3675 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #11720269 | 2 |
| #11720266 | 2 |
| #10591655 | 3 |
| #10588730 | 3 |