Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
236 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 63 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. C9×#817 | C2 | semidirect |
| 3. C3×#63371 | C2 | semidirect |
| 8. #88525 | C4 | semidirect |
| 10. #88521 | C4 | semidirect |
| 19. #63371 | D3 | semidirect |
| 60. #817 | D9 | semidirect |
| 128. C3×C9 | #360 | semidirect |
| 187. C9 | #4518 | semidirect |
| 212. C3 | #10588165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721773 | 2 |
| C9×#817 | 2 |
| C3×#63371 | 2 |
| #10589125 | 3 |
| #10588165 | 3 |