Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
422 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 105 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. C3×C4×Dic18 | C2 | semidirect |
| 3. C2×#88423 | C2 | semidirect |
| 4. C4⋊(C3⋊(C9⋊C8)) | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 25. C4×Dic18 | D3 | semidirect |
| 40. C3×Dic18 | D4 | semidirect |
| 71. C3×C4×C9 | SD16 | semidirect |
| 114. Dic18 | D12 | semidirect |
| 164. C4×C9 | #215 | semidirect |
| 174. C3×C9 | #460 | semidirect |
| 243. C3×C4 | #3672 | semidirect |
| 253. C9 | #5027 | semidirect |
| 285. C4 | #88423 | semidirect |
| 289. C3 | #10588752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#874 | 2 |
| C3×C4×Dic18 | 2 |
| C2×#88423 | 2 |
| C4⋊(C3⋊(C9⋊C8)) | 2 |
| #11720294 | 2 |
| #10590364 | 3 |
| #10588752 | 3 |