Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
421 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 421 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #11722577 | C2 | semidirect |
| 2. #131⋊H(3,𝔽3) | C2 | semidirect |
| 3. C32×#576 | C3 | semidirect |
| 4. C3×#576⋊C3 | C3 | semidirect |
| 9. C3×#994 | C2×C3 | semidirect |
| 14. C3×#131⋊C3 | C2×C3 | semidirect |
| 63. #576 | H(3,𝔽3) | semidirect |
| 159. C32 | #576⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722577 | 2 |
| #131⋊H(3,𝔽3) | 2 |
| C32×#576 | 3 |
| C3×#576⋊C3 | 3 |
| Q16×H(3,𝔽3) | 4 |