Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
590 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 191 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. #11721706 | C2 | semidirect |
| 3. C3×C4×C8×C9 | C2 | semidirect |
| 4. #11720543 | C2 | semidirect |
| 21. C4×C8×C9 | D3 | semidirect |
| 63. C3×C4×C8 | D9 | semidirect |
| 127. C4×C8 | C3⋊D9 | semidirect |
| 128. C3×C9 | #486 | semidirect |
| 182. C9 | #4694 | semidirect |
| 209. C3 | #10588376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721711 | 2 |
| #11721706 | 2 |
| C3×C4×C8×C9 | 2 |
| #11720543 | 2 |
| #10592393 | 3 |
| #10588376 | 3 |