Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1012 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 1012 conjugacy classes of subgroups — too many to draw. Only its 262 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 |
|---|---|---|
| 4. #10592361 | C3 | direct (N × H) |
| 92. C33 | #401 | semidirect |
| 139. C32 | C3⋊#401 | semidirect |
| 140. C32 | C3×#401 | semidirect |
| 164. C3 | C3×C3⋊#401 | semidirect |
| 165. C3 | #10592361 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#95 | 2 |
| C3×#63658 | 2 |
| #10592361 | 3 |
| C3×C3⋊#401 | 3 |