Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
764 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 190 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 |
|---|---|---|
| 5. #10592768 | C3 | direct (N × H) |
| 110. C33 | #491 | semidirect |
| 153. C32 | #5069 | semidirect |
| 154. C32 | C3×#491 | semidirect |
| 173. C3 | C3×#5069 | semidirect |
| 174. C3 | #10592768 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#125 | 2 |
| C3×#64078 | 2 |
| C3×#63637 | 2 |
| C3×#63630 | 2 |
| #10592768 | 3 |
| C3×#5069 | 3 |