Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
2024 conjugacy classes of subgroups; only the 532 normal subgroups are shown.
This group has 2024 conjugacy classes of subgroups — too many to draw. Only its 532 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×A4×H(3,𝔽3) | C2 | direct (N × H) |
| 2. C2×C33×A4 | C3 | semidirect |
| 3. C23×C3×H(3,𝔽3) | C3 | semidirect |
| 4. C2×C3×C22⋊H(3,𝔽3) | C3 | semidirect |
| 5. C2×A4×H(3,𝔽3) | C3 | direct (N × H) |
| 7. C33×A4 | C2×C3 | semidirect |
| 10. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 11. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 12. A4×H(3,𝔽3) | C2×C3 | direct (N × H) |
| 14. C23×C33 | C32 | semidirect |
| 17. C2×C32×A4 | C32 | semidirect |
| 18. C2×C32×A4 | C32 | semidirect |
| 19. C23×H(3,𝔽3) | C32 | semidirect |
| 20. C2×C22⋊H(3,𝔽3) | C32 | semidirect |
| 26. C2×C3×H(3,𝔽3) | A4 | direct (N × H) |
| 29. C22×C33 | C2×C32 | semidirect |
| 32. C32×A4 | C2×C32 | semidirect |
| 33. C32×A4 | C2×C32 | semidirect |
| 36. C22×H(3,𝔽3) | C2×C32 | semidirect |
| 37. C22⋊H(3,𝔽3) | C2×C32 | semidirect |
| 41. C3×H(3,𝔽3) | C2×A4 | direct (N × H) |
| 44. C23×C32 | C33 | semidirect |
| 47. C2×C3×A4 | H(3,𝔽3) | direct (N × H) |
| 49. C2×C3×A4 | C33 | semidirect |
| 56. C2×C33 | C3×A4 | semidirect |
| 60. C2×H(3,𝔽3) | C3×A4 | direct (N × H) |
| 69. C22×C32 | C2×C33 | semidirect |
| 72. C3×A4 | C2×H(3,𝔽3) | direct (N × H) |
| 74. C3×A4 | C2×C33 | semidirect |
| 79. C33 | C2×C3×A4 | semidirect |
| 81. H(3,𝔽3) | C2×C3×A4 | direct (N × H) |
| 83. C23×C3 | C3×H(3,𝔽3) | semidirect |
| 86. C2×A4 | C3×H(3,𝔽3) | direct (N × H) |
| 100. C2×C32 | C32×A4 | semidirect |
| 108. C22×C3 | C2×C3×H(3,𝔽3) | semidirect |
| 111. A4 | C2×C3×H(3,𝔽3) | direct (N × H) |
| 119. C32 | C2×C32×A4 | semidirect |
| 120. C23 | C32×H(3,𝔽3) | semidirect |
| 130. C2×C3 | A4×H(3,𝔽3) | direct (N × H) |
| 134. C22 | C2×C32×H(3,𝔽3) | semidirect |
| 138. C3 | C2×A4×H(3,𝔽3) | direct (N × H) |
| 142. C2 | C3×A4×H(3,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×H(3,𝔽3) | 2 |
| C2×C33×A4 | 3 |
| C23×C3×H(3,𝔽3) | 3 |
| C2×C3×C22⋊H(3,𝔽3) | 3 |
| C2×A4×H(3,𝔽3) | 3 |
| C2×C32×H(3,𝔽3) | 4 |