Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
343 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 343 conjugacy classes of subgroups — too many to draw. Only its 92 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×#131 | C2 | semidirect |
| 3. #63511⋊C3 | C2 | semidirect |
| 4. C2×#3664⋊C3 | C2 | semidirect |
| 5. #63383⋊C3 | C2 | semidirect |
| 6. #63382⋊C3 | C2 | semidirect |
| 7. #63372⋊C3 | C2 | semidirect |
| 9. #10588822 | C3 | semidirect |
| 33. C9×#131 | C2×C3 | semidirect |
| 35. #63511 | C2×C3 | semidirect |
| 36. C2×#3664 | C2×C3 | semidirect |
| 37. #63383 | C2×C3 | semidirect |
| 38. #63382 | C2×C3 | semidirect |
| 39. #63372 | C2×C3 | semidirect |
| 214. #131 | AGL(1,ℤ/9) | semidirect |
| 218. 3−1+2 | #471 | semidirect |
| 295. C9 | C3×#471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#131 | 2 |
| #63512⋊C3 | 2 |
| #63511⋊C3 | 2 |
| C2×#3664⋊C3 | 2 |
| #63383⋊C3 | 2 |
| #63382⋊C3 | 2 |
| #63372⋊C3 | 2 |
| C3×#5141 | 3 |
| #10588822 | 3 |