Finite Group DatabasebetaFinite Group DatabasebetaOrder 4374.
4624 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 4624 conjugacy classes of subgroups — too many to draw. Only its 228 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. C3×#92394 | C3 | semidirect |
| 3. C3×#92392 | C3 | semidirect |
| 4. C33×#272 | C3 | semidirect |
| 5. #13091643 | C3 | direct (N × H) |
| 7. C3×3−1+4 | C2×C3 | semidirect |
| 8. C3×H(5,𝔽3) | C2×C3 | semidirect |
| 9. C33×H(3,𝔽3) | C2×C3 | semidirect |
| 11. #10624930 | C2×C3 | semidirect |
| 15. C32×AΣL(1,𝔽27) | D3 | semidirect |
| 18. #92394 | C32 | semidirect |
| 20. #92392 | C32 | semidirect |
| 26. C32×#272 | C32 | semidirect |
| 31. C35 | C3×D3 | semidirect |
| 35. 3−1+4 | C2×C32 | semidirect |
| 39. H(5,𝔽3) | C2×C32 | semidirect |
| 43. C32×3−1+2 | C3×D3 | semidirect |
| 53. C32×H(3,𝔽3) | C3×D3 | semidirect |
| 55. C32×H(3,𝔽3) | C2×C32 | semidirect |
| 67. C3×AΣL(1,𝔽27) | C3×D3 | semidirect |
| 100. C34 | C32×D3 | semidirect |
| 119. C3×3−1+2 | C32×D3 | semidirect |
| 154. C3×H(3,𝔽3) | C32×D3 | semidirect |
| 326. C3 | #13091643 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#10624930 | 2 |
| C3×#92394 | 3 |
| C3×#92392 | 3 |
| C33×#272 | 3 |
| #13091643 | 3 |
| C3×D3×AΣL(1,𝔽27) | 3 |