Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
250 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 75 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×#97 | C2 | semidirect |
| 3. C9×#803 | C2 | semidirect |
| 19. C9×#97 | D3 | semidirect |
| 30. #4464 | C9 | direct (N × H) |
| 59. C3×#97 | C2×C9 | semidirect |
| 61. #803 | C2×C9 | semidirect |
| 127. #97 | D3×C9 | semidirect |
| 128. C3×C9 | #329 | semidirect |
| 191. C9 | #4464 | direct (N × H) |
| 221. C3 | C9×#329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#875 | 2 |
| C3×C9×#97 | 2 |
| C9×#803 | 2 |
| C3×#4464 | 3 |
| C9×#329 | 3 |