Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
486 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 1. 3−1+2×#127 | C2 | semidirect |
| 2. C2×#3673⋊C3 | C2 | semidirect |
| 3. C2×#3672⋊C3 | C2 | semidirect |
| 4. #63437⋊C3 | C2 | semidirect |
| 5. #63362⋊C3 | C2 | semidirect |
| 7. #10588756 | C3 | semidirect |
| 23. C9×#127 | C2×C3 | semidirect |
| 24. C2×#3673 | C2×C3 | semidirect |
| 25. C2×#3672 | C2×C3 | semidirect |
| 26. #63437 | C2×C3 | semidirect |
| 27. #63362 | C2×C3 | semidirect |
| 38. 3−1+2⋊C8 | D4 | semidirect |
| 107. C9⋊C8 | C3×D4 | semidirect |
| 154. #127 | AGL(1,ℤ/9) | semidirect |
| 157. 3−1+2 | #496 | semidirect |
| 218. C9 | C3×#496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#127 | 2 |
| C2×#3673⋊C3 | 2 |
| C2×#3672⋊C3 | 2 |
| #63437⋊C3 | 2 |
| #63362⋊C3 | 2 |
| C3×#5074 | 3 |
| #10588756 | 3 |