Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
146 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 30 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 |
|---|---|---|
| 4. C9⋊PSU(3,𝔽2) | C3 | direct (N × H) |
| 11. C33×C9 | Q8 | semidirect |
| 32. C32×C9 | C3×Q8 | semidirect |
| 55. C33 | Dic18 | semidirect |
| 66. C3×C9 | PSU(3,𝔽2) | semidirect |
| 92. C32 | C3×Dic18 | semidirect |
| 97. C9 | C3×PSU(3,𝔽2) | semidirect |
| 110. C3 | C9⋊PSU(3,𝔽2) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9⋊#157 | 2 |
| C3×C9×#157 | 2 |
| C3×C3⋊PSU(3,𝔽2) | 3 |
| C9⋊PSU(3,𝔽2) | 3 |
| C3×Dic18 | 9 |