Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
173 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 173 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 4. #10589379 | C3 | semidirect |
| 9. C16×H(3,𝔽3) | C4 | semidirect |
| 33. C32×C16 | Dic3 | semidirect |
| 34. C32×C16 | C3×C4 | semidirect |
| 93. H(3,𝔽3) | #365 | semidirect |
| 121. C16 | (C3⋊Dic3)⋊C3 | semidirect |
| 138. C32 | #4513 | semidirect |
| 139. C32 | C3×#365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×M32 | 2 |
| #63644⋊C3 | 2 |
| #63646⋊C3 | 2 |
| #10589379 | 3 |
| C3×#4513 | 3 |