Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
872 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 152 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. #11723357 | C2 | semidirect |
| 3. C3×#63642 | C2 | semidirect |
| 4. C32×#819 | C2 | semidirect |
| 5. #11722047 | C2 | semidirect |
| 10. #88853 | C4 | semidirect |
| 11. #88852 | C4 | semidirect |
| 12. #88851 | C4 | semidirect |
| 25. #63642 | D3 | semidirect |
| 26. C3×#819 | D3 | semidirect |
| 80. #819 | C3⋊D3 | semidirect |
| 161. C33 | #444 | semidirect |
| 226. C32 | #4717 | semidirect |
| 227. C32 | #4894 | semidirect |
| 254. C3 | #10590918 | semidirect |
| 255. C3 | #10592593 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723945 | 2 |
| #11723357 | 2 |
| C3×#63642 | 2 |
| C32×#819 | 2 |
| #11722047 | 2 |
| #10592593 | 3 |
| #10590918 | 3 |