Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
490 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 30. C3×C8×C9 | Q8 | semidirect |
| 31. C3⋊(C9⋊C8) | Q8 | semidirect |
| 76. C8×C9 | Dic6 | semidirect |
| 112. C3×C9 | #498 | semidirect |
| 123. C3×C8 | Dic18 | semidirect |
| 151. C9 | #4855 | semidirect |
| 158. C8 | #6226 | semidirect |
| 169. C3 | #10588535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721744 | 2 |
| C3×C9×#106 | 2 |
| #11720540 | 2 |
| C8×C3⋊Dic9 | 2 |
| #11720526 | 2 |
| #10592554 | 3 |
| #10588535 | 3 |