Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2100 conjugacy classes of subgroups; only the 795 normal subgroups are shown.
This group has 2100 conjugacy classes of subgroups — too many to draw. Only its 795 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×#88855 | C2 | semidirect |
| 3. #11722206 | C2 | semidirect |
| 4. #11722203 | C2 | semidirect |
| 98. C33 | #413 | semidirect |
| 135. C32 | #5237 | semidirect |
| 162. C3 | #10592936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×#41 | 2 |
| C2×#88855 | 2 |
| #11722206 | 2 |
| #11722203 | 2 |
| #10592936 | 3 |