Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
369 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 369 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 3. #10589426 | C3 | semidirect |
| 119. H(3,𝔽3) | #338 | semidirect |
| 187. C32 | C3⋊#338 | semidirect |
| 188. C32 | C3×#338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×H(3,𝔽3) | 2 |
| C2×#3748⋊C3 | 2 |
| #10589426 | 3 |
| C3×C3⋊#338 | 3 |