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. C3×#63459 | C2 | semidirect |
| 3. C2×#88427 | C2 | semidirect |
| 4. C2×#88416 | C2 | semidirect |
| 5. #11720528 | C2 | semidirect |
| 6. C9×#810 | C2 | semidirect |
| 7. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 35. #63459 | D3 | semidirect |
| 118. #810 | D9 | semidirect |
| 245. C3×C9 | #452 | semidirect |
| 354. C9 | #5047 | semidirect |
| 402. C3 | #10588488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88635 | 2 |
| C3×#63459 | 2 |
| C2×#88427 | 2 |
| C2×#88416 | 2 |
| #11720528 | 2 |
| C9×#810 | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #10590616 | 3 |
| #10588488 | 3 |