Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
300 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. C9×#634 | C3 | semidirect |
| 6. #634⋊C9 | C3 | semidirect |
| 19. C9×H(3,𝔽3) | Q8 | semidirect |
| 23. #634⋊C3 | C9 | direct (N × H) |
| 58. C32×C9 | Dic6 | semidirect |
| 59. C32×C9 | C3×Q8 | semidirect |
| 62. C32⋊C9 | C3×Q8 | semidirect |
| 64. #634 | C3×C9 | semidirect |
| 112. H(3,𝔽3) | Q8×C9 | semidirect |
| 162. C32 | C9×Dic6 | semidirect |
| 163. C32 | C3×Q8×C9 | semidirect |
| 169. C9 | #634⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×H(3,𝔽3) | 2 |
| C9×(C3⋊Dic3)⋊C3 | 2 |
| C9×#634 | 3 |
| C3×#634⋊C3 | 3 |
| C3×C9×Dic6 | 3 |
| #634⋊C9 | 3 |