Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
190 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×3−1+2⋊Q8 | C2 | semidirect |
| 3. M16×3−1+2 | C2 | semidirect |
| 4. #3664⋊C3 | C2 | semidirect |
| 5. Dic36⋊C3 | C2 | semidirect |
| 7. #63471 | C3 | semidirect |
| 23. C2×Dic18 | C2×C3 | semidirect |
| 25. C9×M16 | C2×C3 | semidirect |
| 26. #3664 | C2×C3 | semidirect |
| 27. Dic36 | C2×C3 | semidirect |
| 85. 3−1+2 | #137 | semidirect |
| 116. M16 | AGL(1,ℤ/9) | semidirect |
| 131. C9 | C3×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3697⋊C3 | 2 |
| C2×3−1+2⋊Q8 | 2 |
| M16×3−1+2 | 2 |
| #3664⋊C3 | 2 |
| Dic36⋊C3 | 2 |
| C3×#909 | 3 |
| #63471 | 3 |