Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1736 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 407 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. #11723985 | C2 | semidirect |
| 3. C2×#88863 | C2 | semidirect |
| 6. C2×#88853 | C2 | semidirect |
| 7. #11722185 | C2 | semidirect |
| 124. C33 | #497 | semidirect |
| 166. C32 | #5167 | semidirect |
| 195. C3 | #10592866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×SD16 | 2 |
| #11723985 | 2 |
| C2×#88863 | 2 |
| #11723977 | 2 |
| C2×#88861 | 2 |
| C2×#88853 | 2 |
| #11722185 | 2 |
| #10592866 | 3 |