Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
324 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 120 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. C9×Dic18 | C3 | direct (N × H) |
| 15. C3×C92 | Q8 | semidirect |
| 19. C3×Dic18 | C9 | direct (N × H) |
| 46. C92 | C3×Q8 | semidirect |
| 51. Dic18 | C3×C9 | direct (N × H) |
| 86. C3×C9 | Dic18 | direct (N × H) |
| 87. C3×C9 | Q8×C9 | semidirect |
| 121. C9 | C3×Dic18 | direct (N × H) |
| 122. C9 | C3×Q8×C9 | semidirect |
| 133. C3 | C9×Dic18 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C92 | 2 |
| C3×C9×Dic9 | 2 |
| C3×C9×Dic6 | 3 |
| C32×Dic18 | 3 |
| C9×Dic18 | 3 |