Finite Group DatabasebetaFinite Group DatabasebetaOrder 4374.
5272 conjugacy classes of subgroups; only the 705 normal subgroups are shown.
This group has 5272 conjugacy classes of subgroups — too many to draw. Only its 705 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×#10624930 | C2 | semidirect |
| 2. D3×3−1+4 | C3 | semidirect |
| 3. D3×H(5,𝔽3) | C3 | semidirect |
| 4. C32×D3×H(3,𝔽3) | C3 | semidirect |
| 5. D3×#6909 | C3 | semidirect |
| 6. C3×D3×AΣL(1,𝔽27) | C3 | semidirect |
| 8. C3×3−1+4 | C2×C3 | semidirect |
| 9. C3×H(5,𝔽3) | C2×C3 | semidirect |
| 10. C33×H(3,𝔽3) | C2×C3 | semidirect |
| 16. #10624930 | D3 | direct (N × H) |
| 17. C3×#6909 | C2×C3 | semidirect |
| 18. C32×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 19. C34×D3 | C32 | semidirect |
| 24. C3×D3×3−1+2 | C32 | semidirect |
| 28. C3×D3×H(3,𝔽3) | C32 | semidirect |
| 29. C3×D3×H(3,𝔽3) | C32 | semidirect |
| 32. D3×AΣL(1,𝔽27) | C32 | semidirect |
| 33. D3×AΣL(1,𝔽27) | C32 | semidirect |
| 34. C35 | C2×C32 | semidirect |
| 38. 3−1+4 | C3×D3 | semidirect |
| 42. H(5,𝔽3) | C3×D3 | semidirect |
| 44. C32×3−1+2 | C2×C32 | semidirect |
| 51. C32×H(3,𝔽3) | C3×D3 | semidirect |
| 53. C32×H(3,𝔽3) | C2×C32 | semidirect |
| 54. C32×H(3,𝔽3) | C2×C32 | semidirect |
| 59. #6909 | C3×D3 | semidirect |
| 65. C3×AΣL(1,𝔽27) | C3×D3 | semidirect |
| 66. C3×AΣL(1,𝔽27) | C2×C32 | semidirect |
| 67. C3×AΣL(1,𝔽27) | C2×C32 | semidirect |
| 99. C34 | C32×D3 | semidirect |
| 112. C3×3−1+2 | C32×D3 | semidirect |
| 135. C3×H(3,𝔽3) | C32×D3 | semidirect |
| 136. C3×H(3,𝔽3) | C32×D3 | semidirect |
| 145. AΣL(1,𝔽27) | C32×D3 | semidirect |
| 146. AΣL(1,𝔽27) | C32×D3 | semidirect |
| 292. D3 | #10624930 | direct (N × H) |
| 304. C3 | C2×#10624930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#10624930 | 2 |
| D3×3−1+4 | 3 |
| D3×H(5,𝔽3) | 3 |
| C32×D3×H(3,𝔽3) | 3 |
| D3×#6909 | 3 |
| C3×D3×AΣL(1,𝔽27) | 3 |
| C2×#10624930 | 3 |