Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
234 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 44 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. C3×#131⋊C9 | C2 | semidirect |
| 3. C3×#63422 | C2 | semidirect |
| 5. #10589507 | C3 | direct (N × H) |
| 7. C3×#3689 | C4 | semidirect |
| 8. C3×#3688 | C4 | semidirect |
| 19. #131⋊C9 | C2×C3 | semidirect |
| 20. #63422 | C2×C3 | semidirect |
| 42. #3689 | C3×C4 | semidirect |
| 43. #3688 | C3×C4 | semidirect |
| 51. C3×#131 | D9 | semidirect |
| 126. #131 | C3×D9 | semidirect |
| 228. C3 | #10589507 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63691 | 2 |
| C3×#131⋊C9 | 2 |
| C3×#63422 | 2 |
| C3×#5145 | 3 |
| #10589507 | 3 |
| C3×#3663 | 4 |