Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
162 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 3. #10593251 | C3 | direct (N × H) |
| 13. C3×#622 | C8 | semidirect |
| 14. C33×C8 | C8 | semidirect |
| 15. C3×C3⋊(C3⋊C8) | C8 | semidirect |
| 32. #622 | C3×C8 | semidirect |
| 35. C32×C8 | C3×C8 | semidirect |
| 36. C3⋊(C3⋊C8) | C3×C8 | semidirect |
| 56. C33 | #322 | semidirect |
| 65. C3×C8 | AGL(1,𝔽9) | semidirect |
| 86. C32 | C3×#322 | semidirect |
| 92. C8 | C3×AGL(1,𝔽9) | semidirect |
| 104. C3 | #10593251 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×AGL(1,𝔽9) | 2 |
| C3×C8×#157 | 2 |
| #10593251 | 3 |
| C3×#322 | 9 |