Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
200 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 81 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. C9×#812 | C2 | semidirect |
| 19. C9×M32 | D3 | semidirect |
| 29. #4514 | C9 | direct (N × H) |
| 56. C3×M32 | C2×C9 | semidirect |
| 58. #812 | C2×C9 | semidirect |
| 115. M32 | D3×C9 | semidirect |
| 116. C3×C9 | #349 | semidirect |
| 168. C9 | #4514 | direct (N × H) |
| 192. C3 | C9×#349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×ΓL(1,𝔽25) | 2 |
| C3×C9×M32 | 2 |
| C9×#812 | 2 |
| C3×#4514 | 3 |
| C9×#349 | 3 |