Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
344 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 85 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. #11720571 | C2 | semidirect |
| 3. C3×#63389 | C2 | semidirect |
| 19. #63389 | D3 | semidirect |
| 25. C22×D3×C9 | C8 | semidirect |
| 161. C3×C9 | #323 | semidirect |
| 174. C22×D3 | C9⋊C8 | semidirect |
| 252. C9 | #4468 | semidirect |
| 297. C3 | #10588202 | 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 |
| #11720571 | 2 |
| C3×#63389 | 2 |
| #10589145 | 3 |
| #10588202 | 3 |