Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
249 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 60 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. Dic3⋊AGL(1,𝔽9) | C3 | direct (N × H) |
| 22. C3×C3⋊(C3⋊Dic3) | C8 | semidirect |
| 23. C33×Dic3 | C8 | semidirect |
| 61. C3⋊(C3⋊Dic3) | C3×C8 | semidirect |
| 67. C32×Dic3 | C3×C8 | semidirect |
| 70. C34 | C4⋊C8 | semidirect |
| 127. C3×Dic3 | AGL(1,𝔽9) | semidirect |
| 134. C33 | Dic3⋊C8 | semidirect |
| 135. C33 | C3×C4⋊C8 | semidirect |
| 193. Dic3 | C3×AGL(1,𝔽9) | semidirect |
| 204. C32 | C3×Dic3⋊C8 | semidirect |
| 205. C32 | C4⋊AGL(1,𝔽9) | semidirect |
| 237. C3 | Dic3⋊AGL(1,𝔽9) | direct (N × H) |
| 238. C3 | C3×C4⋊AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊AGL(1,𝔽9) | 2 |
| C2×C32×AGL(1,𝔽9) | 2 |
| C3×Dic3×#157 | 2 |
| C3×C4⋊AGL(1,𝔽9) | 3 |
| Dic3⋊AGL(1,𝔽9) | 3 |
| C3×Dic3⋊C8 | 9 |