Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
173 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 173 conjugacy classes of subgroups — too many to draw. Only its 45 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. C22⋊C4×3−1+2 | C2 | semidirect |
| 3. #3676⋊C3 | C2 | semidirect |
| 5. #63365 | C3 | semidirect |
| 7. C22×AGL(1,ℤ/9) | C4 | semidirect |
| 12. C2×3−1+2⋊C4 | C4 | semidirect |
| 18. C9×C22⋊C4 | C2×C3 | semidirect |
| 19. #3676 | C2×C3 | semidirect |
| 40. C22×D9 | C3×C4 | semidirect |
| 46. C2×Dic9 | C3×C4 | semidirect |
| 82. 3−1+2 | #99 | semidirect |
| 113. C22⋊C4 | AGL(1,ℤ/9) | semidirect |
| 134. C9 | C3×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#611⋊C3 | 2 |
| C22⋊C4×3−1+2 | 2 |
| #3676⋊C3 | 2 |
| C3×#806 | 3 |
| #63365 | 3 |