Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
194 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 2. C3×C9×M32 | C2 | semidirect |
| 3. C2×C3×C9⋊C16 | C2 | semidirect |
| 5. #10588192 | C3 | direct (N × H) |
| 18. C9×M32 | C2×C3 | semidirect |
| 19. C2×C9⋊C16 | C2×C3 | semidirect |
| 54. C3×M32 | D9 | semidirect |
| 111. M32 | C3×D9 | semidirect |
| 113. C3×C9 | #350 | semidirect |
| 163. C9 | C3×#350 | semidirect |
| 186. C3 | #10588192 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63464 | 2 |
| C3×C9×M32 | 2 |
| C2×C3×C9⋊C16 | 2 |
| C3×#4515 | 3 |
| #10588192 | 3 |