Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1080 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 270 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. C32×#634 | C3 | semidirect |
| 5. C3×#634⋊C3 | C3 | direct (N × H) |
| 15. C32×H(3,𝔽3) | Q8 | semidirect |
| 17. C3×#634 | C32 | semidirect |
| 21. #634⋊C3 | C32 | direct (N × H) |
| 47. C34 | Dic6 | semidirect |
| 48. C34 | C3×Q8 | semidirect |
| 50. C3×H(3,𝔽3) | C3×Q8 | semidirect |
| 53. #634 | C33 | semidirect |
| 100. C33 | C3×Dic6 | semidirect |
| 101. C33 | C32×Q8 | semidirect |
| 103. H(3,𝔽3) | C32×Q8 | semidirect |
| 145. C32 | #634⋊C3 | direct (N × H) |
| 147. C32 | C32×Dic6 | semidirect |
| 148. C32 | C33×Q8 | semidirect |
| 164. C3 | C3×#634⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×H(3,𝔽3) | 2 |
| C32×(C3⋊Dic3)⋊C3 | 2 |
| C32×#634 | 3 |
| C33×Dic6 | 3 |
| C3×#634⋊C3 | 3 |