Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
689 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 689 conjugacy classes of subgroups — too many to draw. Only its 108 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. C3×#66321 | C2 | direct (N × H) |
| 4. C2×C3×#1084 | C3 | semidirect |
| 5. C2×#66321 | C3 | direct (N × H) |
| 6. C2×C3×AΣL(1,𝔽27) | C4 | semidirect |
| 12. C3×#1084 | C2×C3 | semidirect |
| 15. #66321 | C2×C3 | direct (N × H) |
| 16. C3×AΣL(1,𝔽27) | C2×C4 | semidirect |
| 22. C2×#1084 | C32 | semidirect |
| 23. C2×C34 | Dic3 | semidirect |
| 27. C2×C3×H(3,𝔽3) | C3×C4 | semidirect |
| 31. C2×AΣL(1,𝔽27) | C3×C4 | semidirect |
| 50. #1084 | C2×C32 | semidirect |
| 51. C34 | C2×Dic3 | semidirect |
| 53. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 55. AΣL(1,𝔽27) | C2×C3×C4 | semidirect |
| 73. C2×C33 | C3×Dic3 | semidirect |
| 84. C2×H(3,𝔽3) | C32×C4 | semidirect |
| 113. C33 | C2×C3×Dic3 | semidirect |
| 118. H(3,𝔽3) | C2×C32×C4 | semidirect |
| 184. C2×C3 | #66321 | direct (N × H) |
| 195. C3 | C2×#66321 | direct (N × H) |
| 197. C2 | C3×#66321 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×AΣL(1,𝔽27) | 2 |
| C3×#66321 | 2 |
| C2×C33×Dic3 | 3 |
| C2×C3×#1084 | 3 |
| C2×#66321 | 3 |