Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1792 conjugacy classes of subgroups; only the 353 normal subgroups are shown.
This group has 1792 conjugacy classes of subgroups — too many to draw. Only its 353 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×#88861 | C2 | semidirect |
| 3. C2×#88851 | C2 | semidirect |
| 4. #11723928 | C2 | semidirect |
| 5. C33×#102 | C2 | semidirect |
| 6. #11722184 | C2 | semidirect |
| 7. #11722179 | C2 | semidirect |
| 26. C32×#102 | D3 | semidirect |
| 43. #6308 | D4 | semidirect |
| 72. C3⋊(C3⋊Dic3) | SD16 | semidirect |
| 77. C3×#102 | C3⋊D3 | semidirect |
| 135. #102 | C3⋊(C3⋊D3) | semidirect |
| 136. C33 | #460 | semidirect |
| 185. C32 | #4762 | semidirect |
| 221. C3 | #10592461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723981 | 2 |
| C2×#88861 | 2 |
| C2×#88851 | 2 |
| #11723928 | 2 |
| C33×#102 | 2 |
| #11722184 | 2 |
| #11722179 | 2 |
| #10592461 | 3 |