Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
728 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 1. C3×#66363 | C2 | direct (N × H) |
| 2. C2×C33×A4 | C3 | semidirect |
| 3. C23×C3×H(3,𝔽3) | C3 | semidirect |
| 4. C2×C3×#1094 | C3 | semidirect |
| 5. C2×#66363 | C3 | direct (N × H) |
| 7. C33×A4 | C2×C3 | semidirect |
| 10. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 11. C3×#1094 | C2×C3 | semidirect |
| 12. #66363 | C2×C3 | direct (N × H) |
| 19. C2×C32×A4 | C32 | semidirect |
| 21. C23×H(3,𝔽3) | C32 | semidirect |
| 23. C2×#1094 | C32 | semidirect |
| 29. C2×C3×H(3,𝔽3) | A4 | semidirect |
| 40. C32×A4 | C2×C32 | semidirect |
| 46. C22×H(3,𝔽3) | C2×C32 | semidirect |
| 48. #1094 | C2×C32 | semidirect |
| 52. C3×H(3,𝔽3) | C2×A4 | semidirect |
| 82. C2×H(3,𝔽3) | C3×A4 | semidirect |
| 116. H(3,𝔽3) | C2×C3×A4 | semidirect |
| 121. C23×C3 | AΣL(1,𝔽27) | semidirect |
| 160. C22×C3 | C2×AΣL(1,𝔽27) | semidirect |
| 174. C23 | C3×AΣL(1,𝔽27) | semidirect |
| 189. C2×C3 | #66363 | direct (N × H) |
| 193. C22 | C2×C3×AΣL(1,𝔽27) | semidirect |
| 198. C3 | C2×#66363 | direct (N × H) |
| 202. C2 | C3×#66363 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66363 | 2 |
| C2×C33×A4 | 3 |
| C23×C3×H(3,𝔽3) | 3 |
| C2×C3×#1094 | 3 |
| C2×#66363 | 3 |
| C2×C3×AΣL(1,𝔽27) | 4 |