Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11721866 | C2 | semidirect |
| 3. #11721865 | C2 | semidirect |
| 4. C2×#88543 | C2 | semidirect |
| 5. #11720575 | C2 | semidirect |
| 6. #11720556 | C2 | semidirect |
| 7. #11720555 | C2 | semidirect |
| 199. C3×C9 | #471 | semidirect |
| 272. C9 | #5200 | semidirect |
| 305. C3 | #10588878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×AGL(1,ℤ/8) | 2 |
| #11721866 | 2 |
| #11721865 | 2 |
| C2×#88543 | 2 |
| #11720575 | 2 |
| #11720556 | 2 |
| #11720555 | 2 |
| #10592899 | 3 |
| #10588878 | 3 |