Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
516 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 13. C9×H(3,𝔽3) | Q8 | semidirect |
| 34. C32×C9 | Dic6 | semidirect |
| 35. C32⋊C9 | Dic6 | semidirect |
| 60. H(3,𝔽3) | Dic18 | semidirect |
| 84. C32 | #6226 | semidirect |
| 88. C9 | #6229 | semidirect |
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⋊#1084 | 2 |
| #10619988 | 3 |
| C3×#6226 | 3 |
| #10619654 | 3 |