Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
247 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 247 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×C4×AGL(1,ℤ/9) | C2 | semidirect |
| 3. C4⋊C4×3−1+2 | C2 | semidirect |
| 4. (C2×AGL(1,ℤ/9))⋊C4 | C2 | semidirect |
| 5. (C2×AGL(1,ℤ/9))⋊C4 | C2 | semidirect |
| 6. (C2×AGL(1,ℤ/9))⋊C4 | C2 | semidirect |
| 7. (3−1+2⋊C4)⋊C4 | C2 | semidirect |
| 9. #63456 | C3 | semidirect |
| 27. C2×C4×D9 | C2×C3 | semidirect |
| 29. C9×C4⋊C4 | C2×C3 | semidirect |
| 30. (C2×D9)⋊C4 | C2×C3 | semidirect |
| 31. (C2×D9)⋊C4 | C2×C3 | semidirect |
| 32. (C2×D9)⋊C4 | C2×C3 | semidirect |
| 33. Dic9⋊C4 | C2×C3 | semidirect |
| 117. 3−1+2 | #123 | semidirect |
| 152. C4⋊C4 | AGL(1,ℤ/9) | semidirect |
| 182. C9 | C3×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊AGL(1,ℤ/9) | 2 |
| C2×C4×AGL(1,ℤ/9) | 2 |
| C4⋊C4×3−1+2 | 2 |
| (C2×AGL(1,ℤ/9))⋊C4 | 2 |
| (3−1+2⋊C4)⋊C4 | 2 |
| C3×#894 | 3 |
| #63456 | 3 |