Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
788 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 254 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 | direct (N × H) |
| 110. C33 | #338 | semidirect |
| 165. C32 | C3⋊#338 | semidirect |
| 166. C32 | C3×#338 | semidirect |
| 190. C3 | C3×C3⋊#338 | semidirect |
| 191. C3 | #10589426 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| C2×C3×#3748 | 2 |
| #10589426 | 3 |
| C3×C3⋊#338 | 3 |