Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
258 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 70 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. Q16×AGL(1,ℤ/9) | C2 | semidirect |
| 3. 3−1+2×Q32 | C2 | semidirect |
| 4. #63388⋊C3 | C2 | semidirect |
| 5. #63387⋊C3 | C2 | semidirect |
| 6. #63359⋊C3 | C2 | semidirect |
| 7. #63357⋊C3 | C2 | semidirect |
| 9. #10588598 | C3 | semidirect |
| 29. Q16×D9 | C2×C3 | semidirect |
| 31. C9×Q32 | C2×C3 | semidirect |
| 32. #63388 | C2×C3 | semidirect |
| 33. #63387 | C2×C3 | semidirect |
| 34. #63359 | C2×C3 | semidirect |
| 35. #63357 | C2×C3 | semidirect |
| 166. Q32 | AGL(1,ℤ/9) | semidirect |
| 170. 3−1+2 | #510 | semidirect |
| 227. C9 | C3×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63481⋊C3 | 2 |
| Q16×AGL(1,ℤ/9) | 2 |
| 3−1+2×Q32 | 2 |
| #63388⋊C3 | 2 |
| #63387⋊C3 | 2 |
| #63359⋊C3 | 2 |
| #63357⋊C3 | 2 |
| C3×#4918 | 3 |
| #10588598 | 3 |