Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
270 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 5. Dic18⋊C9 | C3 | direct (N × H) |
| 15. C3×C9⋊C9 | Q8 | semidirect |
| 19. C3×Dic18 | C9 | semidirect |
| 45. C9⋊C9 | C3×Q8 | semidirect |
| 50. Dic18 | C3×C9 | semidirect |
| 83. C3×C9 | Q8×C9 | semidirect |
| 116. C9 | C3×Q8×C9 | semidirect |
| 127. C3 | Dic18⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C9⋊C9 | 2 |
| C3×Dic9⋊C9 | 2 |
| C3×C9×Dic6 | 3 |
| C32×Dic18 | 3 |
| Dic18⋊C9 | 3 |