Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
306 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 44. C3⋊(C9⋊C8) | Q8 | semidirect |
| 45. C3×C9⋊C8 | Q8 | semidirect |
| 120. C9⋊C8 | Dic6 | semidirect |
| 180. C3×C9 | #501 | semidirect |
| 250. C9 | #4856 | semidirect |
| 280. C3 | #10588761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#888 | 2 |
| #11720927 | 2 |
| #11720525 | 2 |
| C3×#63367 | 2 |
| #11720265 | 2 |
| #11720262 | 2 |
| #11720258 | 2 |
| #10590421 | 3 |
| #10588761 | 3 |