Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
459 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 459 conjugacy classes of subgroups — too many to draw. Only its 72 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 | semidirect |
| 15. C32⋊H(3,𝔽3) | Q8 | semidirect |
| 52. C34 | C3×Q8 | semidirect |
| 55. C3×H(3,𝔽3) | Dic6 | semidirect |
| 56. C3×H(3,𝔽3) | C3×Q8 | semidirect |
| 59. #634 | H(3,𝔽3) | semidirect |
| 122. C33 | C3×Dic6 | semidirect |
| 196. C32 | #634⋊C3 | semidirect |
| 197. C32 | 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×C32⋊H(3,𝔽3) | 2 |
| (C3⋊Dic3)⋊H(3,𝔽3) | 2 |
| C32×#634 | 3 |
| Dic6×H(3,𝔽3) | 3 |
| C3×#634⋊C3 | 3 |