Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
412 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 112 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×#3664⋊C3 | C2 | semidirect |
| 3. C2×Dic36⋊C3 | C2 | semidirect |
| 4. #63437⋊C3 | C2 | semidirect |
| 5. C4×C8×3−1+2 | C2 | semidirect |
| 7. #10588378 | C3 | semidirect |
| 23. C2×#3664 | C2×C3 | semidirect |
| 24. C2×Dic36 | C2×C3 | semidirect |
| 25. #63437 | C2×C3 | semidirect |
| 27. C4×C8×C9 | C2×C3 | semidirect |
| 146. C4×C8 | AGL(1,ℤ/9) | semidirect |
| 147. 3−1+2 | #495 | semidirect |
| 201. C9 | C3×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D72⋊C3 | 2 |
| C2×#3664⋊C3 | 2 |
| C2×Dic36⋊C3 | 2 |
| #63437⋊C3 | 2 |
| C4×C8×3−1+2 | 2 |
| C3×#4696 | 3 |
| #10588378 | 3 |