Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
254 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 254 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 |
|---|---|---|
| 25. C3×AGL(1,𝔽9) | Q8 | semidirect |
| 26. #6308 | C8 | semidirect |
| 28. C32×Dic6 | C8 | semidirect |
| 29. #6293 | C8 | semidirect |
| 60. AGL(1,𝔽9) | Dic6 | direct (N × H) |
| 106. C33 | C8×Q8 | semidirect |
| 120. Dic6 | AGL(1,𝔽9) | direct (N × H) |
| 157. C32 | C8×Dic6 | semidirect |
| 187. C3 | Q8×AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic6×#157 | 2 |
| C4⋊(C3⋊AGL(1,𝔽9)) | 2 |
| C3×C4×AGL(1,𝔽9) | 2 |
| Dic3⋊AGL(1,𝔽9) | 2 |
| Dic3×AGL(1,𝔽9) | 2 |
| Q8×AGL(1,𝔽9) | 3 |
| C8×Dic6 | 9 |