Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
300 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 4. C32×Dic18 | C3 | semidirect |
| 11. C9×H(3,𝔽3) | Q8 | semidirect |
| 31. C32×C9 | C3×Q8 | semidirect |
| 36. Dic18 | H(3,𝔽3) | direct (N × H) |
| 58. H(3,𝔽3) | Dic18 | direct (N × H) |
| 85. C32 | C3×Dic18 | semidirect |
| 89. C9 | Q8×H(3,𝔽3) | 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 |
| H(3,𝔽3)×Dic9 | 2 |
| Dic6×H(3,𝔽3) | 3 |
| C32×Dic18 | 3 |