Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
224 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 2. C3×#64218 | C2 | semidirect |
| 3. C2×C3×#3771 | C2 | semidirect |
| 4. C3×#64214 | C2 | semidirect |
| 5. C3×#64213 | C2 | semidirect |
| 6. #10596485 | C3 | direct (N × H) |
| 16. #64218 | C2×C3 | semidirect |
| 17. C2×#3771 | C2×C3 | semidirect |
| 18. #64214 | C2×C3 | semidirect |
| 19. #64213 | C2×C3 | semidirect |
| 92. C33 | #504 | semidirect |
| 137. C32 | C3×#504 | semidirect |
| 161. C3 | #10596485 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64287 | 2 |
| C3×#64218 | 2 |
| C2×C3×#3771 | 2 |
| C3×#64214 | 2 |
| C3×#64213 | 2 |
| #10596485 | 3 |
| C3×#504 | 9 |