Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
234 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 47 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. C4⋊(C3⋊AGL(1,𝔽9)) | C2 | semidirect |
| 3. C4×C3⋊AGL(1,𝔽9) | C2 | semidirect |
| 23. C33×D4 | C8 | semidirect |
| 25. C3×C4⋊(C3⋊D3) | C8 | semidirect |
| 61. C32×D4 | C3⋊C8 | semidirect |
| 63. C4⋊(C3⋊D3) | C3⋊C8 | semidirect |
| 105. C33 | D4⋊C8 | semidirect |
| 112. C3×D4 | AGL(1,𝔽9) | semidirect |
| 165. C32 | D4⋊(C3⋊C8) | semidirect |
| 169. D4 | C3⋊AGL(1,𝔽9) | semidirect |
| 203. C3 | D4⋊AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×#157 | 2 |
| C4⋊(C3⋊AGL(1,𝔽9)) | 2 |
| C4×C3⋊AGL(1,𝔽9) | 2 |
| D4⋊AGL(1,𝔽9) | 3 |
| D4⋊(C3⋊C8) | 9 |