Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
385 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 385 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3672⋊C3 | C2 | semidirect |
| 3. C2×#3663⋊C3 | C2 | semidirect |
| 4. #63459⋊C3 | C2 | semidirect |
| 5. 3−1+2×#102 | C2 | semidirect |
| 6. #63376⋊C3 | C2 | semidirect |
| 7. #63366⋊C3 | C2 | semidirect |
| 9. #10588460 | C3 | semidirect |
| 31. C2×#3672 | C2×C3 | semidirect |
| 32. C2×#3663 | C2×C3 | semidirect |
| 33. #63459 | C2×C3 | semidirect |
| 35. C9×#102 | C2×C3 | semidirect |
| 36. #63376 | C2×C3 | semidirect |
| 37. #63366 | C2×C3 | semidirect |
| 53. 3−1+2⋊C8 | D4 | semidirect |
| 149. C9⋊C8 | C3×D4 | semidirect |
| 221. #102 | AGL(1,ℤ/9) | semidirect |
| 222. 3−1+2 | #468 | semidirect |
| 310. C9 | C3×#468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63500⋊C3 | 2 |
| C2×#3672⋊C3 | 2 |
| C2×#3663⋊C3 | 2 |
| #63459⋊C3 | 2 |
| 3−1+2×#102 | 2 |
| #63376⋊C3 | 2 |
| #63366⋊C3 | 2 |
| C3×#4780 | 3 |
| #10588460 | 3 |