Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1084 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1084 conjugacy classes of subgroups — too many to draw. Only its 188 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. C2×C3×#3746 | C2 | semidirect |
| 3. #11723441 | C2 | semidirect |
| 4. C2×#88797 | C2 | semidirect |
| 5. C32×C8×Dic3 | C2 | semidirect |
| 17. C2×#3746 | D3 | semidirect |
| 27. C3×C8×Dic3 | D3 | semidirect |
| 78. C8×Dic3 | C3⋊D3 | semidirect |
| 153. C33 | #495 | semidirect |
| 217. C32 | #4696 | semidirect |
| 218. C32 | #5191 | semidirect |
| 246. C3 | #10590865 | semidirect |
| 247. C3 | #10592395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88852 | 2 |
| C2×C3×#3746 | 2 |
| #11723441 | 2 |
| C2×#88797 | 2 |
| C32×C8×Dic3 | 2 |
| #10592395 | 3 |
| #10590865 | 3 |