Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 93 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×C22⋊C8 | C2 | semidirect |
| 3. C9×#830 | C2 | semidirect |
| 19. C9×C22⋊C8 | D3 | semidirect |
| 25. C22×D3×C9 | C8 | semidirect |
| 34. #4468 | C9 | direct (N × H) |
| 68. C3×C22⋊C8 | C2×C9 | semidirect |
| 70. #830 | C2×C9 | semidirect |
| 160. C22⋊C8 | D3×C9 | semidirect |
| 161. C3×C9 | #323 | semidirect |
| 174. C22×D3 | C8×C9 | semidirect |
| 252. C9 | #4468 | direct (N × H) |
| 297. C3 | C9×#323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×(C2×D3)⋊C4 | 2 |
| C3×C9×C22⋊C8 | 2 |
| C9×#830 | 2 |
| C3×#4468 | 3 |
| C9×#323 | 3 |