Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
420 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 83 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. #131⋊H(3,𝔽3) | C2 | semidirect |
| 3. C32×#568 | C3 | semidirect |
| 4. C3×#568⋊C3 | C3 | semidirect |
| 12. C32×#131 | C2×C3 | semidirect |
| 15. C3×#131⋊C3 | C2×C3 | semidirect |
| 71. #568 | H(3,𝔽3) | semidirect |
| 117. #131 | C2×H(3,𝔽3) | semidirect |
| 191. C32 | #568⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41⋊H(3,𝔽3) | 2 |
| #131⋊H(3,𝔽3) | 2 |
| C32×#568 | 3 |
| C3×#568⋊C3 | 3 |
| M16×H(3,𝔽3) | 4 |