Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
261 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 77 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. C22×C4×3−1+2 | C2 | semidirect |
| 3. #3676⋊C3 | C2 | semidirect |
| 4. (C2×AGL(1,ℤ/9))⋊C4 | C2 | semidirect |
| 5. (3−1+2⋊C4)⋊C4 | C2 | semidirect |
| 7. #63491 | C3 | semidirect |
| 21. C22×C4×C9 | C2×C3 | semidirect |
| 23. #3676 | C2×C3 | semidirect |
| 24. (C2×D9)⋊C4 | C2×C3 | semidirect |
| 25. Dic9⋊C4 | C2×C3 | semidirect |
| 88. 3−1+2 | #123 | semidirect |
| 115. C22×C4 | AGL(1,ℤ/9) | semidirect |
| 137. C9 | C3×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×3−1+2 | 2 |
| C2×#611⋊C3 | 2 |
| #3676⋊C3 | 2 |
| (C2×AGL(1,ℤ/9))⋊C4 | 2 |
| (3−1+2⋊C4)⋊C4 | 2 |
| C3×#929 | 3 |
| #63491 | 3 |