Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
896 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 170 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. C3×#64160 | C2 | semidirect |
| 3. C3×#64157 | C2 | semidirect |
| 4. C2×C3×#3754 | C2 | semidirect |
| 5. C3×#63660 | C2 | semidirect |
| 6. C3×#63651 | C2 | semidirect |
| 7. C3×#63649 | C2 | semidirect |
| 8. #10592899 | C3 | direct (N × H) |
| 28. #64160 | C2×C3 | semidirect |
| 29. #64157 | C2×C3 | semidirect |
| 30. C2×#3754 | C2×C3 | semidirect |
| 34. #63660 | C2×C3 | semidirect |
| 35. #63651 | C2×C3 | semidirect |
| 36. #63649 | C2×C3 | semidirect |
| 227. C33 | #471 | semidirect |
| 320. C32 | #5200 | semidirect |
| 321. C32 | C3×#471 | semidirect |
| 359. C3 | C3×#5200 | semidirect |
| 360. C3 | #10592899 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×AGL(1,ℤ/8) | 2 |
| C3×#64160 | 2 |
| C3×#64157 | 2 |
| C2×C3×#3754 | 2 |
| C3×#63660 | 2 |
| C3×#63651 | 2 |
| C3×#63649 | 2 |
| #10592899 | 3 |
| C3×#5200 | 3 |