Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
466 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 4. C4×C9×C3⋊C8 | C2 | semidirect |
| 5. C3×#63362 | C2 | semidirect |
| 6. #11720275 | C2 | semidirect |
| 7. #11720271 | C2 | semidirect |
| 19. #88414 | C4 | semidirect |
| 20. (C3⋊D9)⋊C8 | C4 | semidirect |
| 35. #63362 | D3 | semidirect |
| 98. C4×C3⋊C8 | D9 | semidirect |
| 190. C3×C9 | #405 | semidirect |
| 266. C9 | #4708 | semidirect |
| 296. C3 | #10588371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721709 | 2 |
| C2×#88414 | 2 |
| C2×(C3⋊D9)⋊C8 | 2 |
| C4×C9×C3⋊C8 | 2 |
| C3×#63362 | 2 |
| #11720275 | 2 |
| #11720271 | 2 |
| #10590321 | 3 |
| #10588371 | 3 |