Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
390 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 11. C9×H(3,𝔽3) | Q8 | semidirect |
| 14. #6229 | C9 | direct (N × H) |
| 30. C32×C9 | Dic6 | semidirect |
| 57. H(3,𝔽3) | Q8×C9 | semidirect |
| 84. C32 | C9×Dic6 | semidirect |
| 87. C9 | #6229 | 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×#1084 | 2 |
| C3×#6229 | 3 |
| C3×C9×Dic6 | 3 |