Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. C4×#6909 | C2 | semidirect |
| 3. #66322⋊C3 | C2 | semidirect |
| 4. C4×C3⋊((C3⋊D3)⋊C3) | C3 | semidirect |
| 6. C4×#4175 | C3 | semidirect |
| 8. #4175⋊C3 | C4 | direct (N × H) |
| 12. C3×C4×H(3,𝔽3) | D3 | semidirect |
| 13. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 14. C3⋊((C3⋊Dic3)⋊C3) | C2×C3 | semidirect |
| 18. C4×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 19. #66322 | C2×C3 | semidirect |
| 20. #6909 | C2×C4 | semidirect |
| 21. C4×C3⋊(C3⋊D3) | C32 | semidirect |
| 29. C3⋊((C3⋊D3)⋊C3) | C3×C4 | semidirect |
| 33. #4175 | C3×C4 | semidirect |
| 40. C33×C4 | C2×C32 | semidirect |
| 41. C3⋊(C3⋊Dic3) | C2×C32 | semidirect |
| 57. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 58. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 60. AΣL(1,𝔽27) | C2×C3×C4 | semidirect |
| 72. C3⋊(C3⋊D3) | C32×C4 | semidirect |
| 114. C33 | C2×C32×C4 | semidirect |
| 191. C4 | #4175⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4175⋊C3 | 2 |
| C4×#6909 | 2 |
| #66322⋊C3 | 2 |
| C4×C3⋊((C3⋊D3)⋊C3) | 3 |
| C3×C4×(C3⋊D3)⋊C3 | 3 |
| C4×#4175 | 3 |