Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
347 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 347 conjugacy classes of subgroups — too many to draw. Only its 80 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. #63495⋊C3 | C2 | semidirect |
| 2. C2×#3673⋊C3 | C2 | semidirect |
| 3. #63470⋊C3 | C2 | semidirect |
| 4. #63469⋊C3 | C2 | semidirect |
| 5. 3−1+2×#100 | C2 | semidirect |
| 6. #63383⋊C3 | C2 | semidirect |
| 7. #63381⋊C3 | C2 | semidirect |
| 9. #10588429 | C3 | semidirect |
| 32. #63495 | C2×C3 | semidirect |
| 33. C2×#3673 | C2×C3 | semidirect |
| 34. #63470 | C2×C3 | semidirect |
| 35. #63469 | C2×C3 | semidirect |
| 37. C9×#100 | C2×C3 | semidirect |
| 38. #63383 | C2×C3 | semidirect |
| 39. #63381 | C2×C3 | semidirect |
| 217. #100 | AGL(1,ℤ/9) | semidirect |
| 218. 3−1+2 | #472 | semidirect |
| 299. C9 | C3×#472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63495⋊C3 | 2 |
| C2×#3673⋊C3 | 2 |
| #63470⋊C3 | 2 |
| #63469⋊C3 | 2 |
| 3−1+2×#100 | 2 |
| #63383⋊C3 | 2 |
| #63381⋊C3 | 2 |
| C3×#4749 | 3 |
| #10588429 | 3 |