Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
246 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 5. AGL(1,𝔽9)⋊Q8 | C3 | direct (N × H) |
| 22. C3×AGL(1,𝔽9) | Q8 | semidirect |
| 52. AGL(1,𝔽9) | C3×Q8 | semidirect |
| 94. C33 | #498 | semidirect |
| 141. C32 | C3×#498 | semidirect |
| 167. C3 | AGL(1,𝔽9)⋊Q8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4⋊PSU(3,𝔽2) | 2 |
| C3×#64222 | 2 |
| C3×C4×AGL(1,𝔽9) | 2 |
| C3×AGL(1,𝔽9)⋊C4 | 2 |
| AGL(1,𝔽9)⋊Q8 | 3 |
| C3×#498 | 9 |