Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
448 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 448 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. #63511⋊C3 | C2 | semidirect |
| 3. #63471⋊C3 | C2 | semidirect |
| 4. #63431⋊C3 | C2 | semidirect |
| 5. 3−1+2×#104 | C2 | semidirect |
| 6. #63382⋊C3 | C2 | semidirect |
| 7. #63364⋊C3 | C2 | semidirect |
| 9. #10588506 | C3 | semidirect |
| 35. #63511 | C2×C3 | semidirect |
| 36. #63471 | C2×C3 | semidirect |
| 37. #63431 | C2×C3 | semidirect |
| 39. C9×#104 | C2×C3 | semidirect |
| 40. #63382 | C2×C3 | semidirect |
| 41. #63364 | C2×C3 | semidirect |
| 248. #104 | AGL(1,ℤ/9) | semidirect |
| 250. 3−1+2 | #456 | semidirect |
| 345. C9 | C3×#456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722642 | 2 |
| #63511⋊C3 | 2 |
| #63471⋊C3 | 2 |
| #63431⋊C3 | 2 |
| 3−1+2×#104 | 2 |
| #63382⋊C3 | 2 |
| #63364⋊C3 | 2 |
| C3×#4826 | 3 |
| #10588506 | 3 |