Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1344 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 403 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 |
|---|---|---|
| 3. #11722205 | C2 | semidirect |
| 4. #11722205 | C2 | semidirect |
| 6. #11722178 | C2 | semidirect |
| 7. #11722177 | C2 | semidirect |
| 117. C33 | #485 | semidirect |
| 157. C32 | #5045 | semidirect |
| 186. C3 | #10592744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C22⋊Q8 | 2 |
| #11723967 | 2 |
| #11722205 | 2 |
| #11722200 | 2 |
| #11722178 | 2 |
| #11722177 | 2 |
| #10592744 | 3 |