Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
476 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. #11722630 | C2 | semidirect |
| 2. 3−1+2×#124 | C2 | semidirect |
| 3. #63495⋊C3 | C2 | semidirect |
| 4. #63394⋊C3 | C2 | semidirect |
| 5. #63364⋊C3 | C2 | semidirect |
| 7. #10588742 | C3 | semidirect |
| 22. #63713 | C2×C3 | semidirect |
| 26. C9×#124 | C2×C3 | semidirect |
| 27. #63495 | C2×C3 | semidirect |
| 28. #63394 | C2×C3 | semidirect |
| 29. #63364 | C2×C3 | semidirect |
| 175. #124 | AGL(1,ℤ/9) | semidirect |
| 178. 3−1+2 | #454 | semidirect |
| 247. C9 | C3×#454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722630 | 2 |
| 3−1+2×#124 | 2 |
| #63495⋊C3 | 2 |
| #63394⋊C3 | 2 |
| #63364⋊C3 | 2 |
| C3×#5062 | 3 |
| #10588742 | 3 |