Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
380 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11720935 | C2 | semidirect |
| 3. #11720543 | C2 | semidirect |
| 4. C9×#821 | C2 | semidirect |
| 5. C3×#63375 | C2 | semidirect |
| 6. #11720295 | C2 | semidirect |
| 7. #11720267 | C2 | semidirect |
| 34. #63375 | D3 | semidirect |
| 103. #821 | D9 | semidirect |
| 213. C3×C9 | #490 | semidirect |
| 310. C9 | #4713 | semidirect |
| 354. C3 | #10588444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721040 | 2 |
| #11720935 | 2 |
| #11720543 | 2 |
| C9×#821 | 2 |
| C3×#63375 | 2 |
| #11720295 | 2 |
| #11720267 | 2 |
| #10590882 | 3 |
| #10588444 | 3 |