Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
165 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 165 conjugacy classes of subgroups — too many to draw. Only its 43 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. C32×#504 | C3 | semidirect |
| 3. C3×#504⋊C3 | C3 | semidirect |
| 37. #504 | H(3,𝔽3) | semidirect |
| 87. C32 | #504⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131⋊H(3,𝔽3) | 2 |
| C32×#504 | 3 |
| C3×#504⋊C3 | 3 |
| C16×H(3,𝔽3) | 4 |