Finite Group DatabasebetaFinite Group DatabasebetaOrder 3888.
2776 conjugacy classes of subgroups; only the 426 normal subgroups are shown.
This group has 2776 conjugacy classes of subgroups — too many to draw. Only its 426 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. C24×C3×3−1+2 | C3 | semidirect |
| 3. C3×#88907 | C3 | semidirect |
| 4. 3−1+2×C22⋊A4 | C3 | direct (N × H) |
| 5. C3×C9⋊(C22⋊A4) | C3 | semidirect |
| 6. C3×C9×C22⋊A4 | C3 | semidirect |
| 14. C24×3−1+2 | C32 | semidirect |
| 15. C24×C3×C9 | C32 | semidirect |
| 16. #88907 | C32 | semidirect |
| 17. C3×C22⋊(C22⋊C9) | C32 | semidirect |
| 18. C9⋊(C22⋊A4) | C32 | semidirect |
| 19. C9×C22⋊A4 | C32 | semidirect |
| 22. C22×C3×3−1+2 | A4 | semidirect |
| 37. C3×C22⋊A4 | 3−1+2 | direct (N × H) |
| 40. C24×C9 | C33 | semidirect |
| 41. C22⋊(C22⋊C9) | C33 | semidirect |
| 49. C22×3−1+2 | C3×A4 | semidirect |
| 51. C22×C3×C9 | C3×A4 | semidirect |
| 60. C3×3−1+2 | C22⋊A4 | direct (N × H) |
| 70. C24×C3 | C3×3−1+2 | semidirect |
| 73. C22⋊A4 | C3×3−1+2 | direct (N × H) |
| 86. C22×C9 | C32×A4 | semidirect |
| 95. 3−1+2 | C3×C22⋊A4 | direct (N × H) |
| 98. C3×C9 | C3×C22⋊A4 | semidirect |
| 106. C24 | C32×3−1+2 | semidirect |
| 111. C22×C3 | A4×3−1+2 | semidirect |
| 124. C9 | C32×C22⋊A4 | semidirect |
| 130. C22 | C3×A4×3−1+2 | semidirect |
| 134. C3 | 3−1+2×C22⋊A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C22⋊A4 | 3 |
| C24×C3×3−1+2 | 3 |
| C3×#88907 | 3 |
| 3−1+2×C22⋊A4 | 3 |
| C3×C9⋊(C22⋊A4) | 3 |
| C3×C9×C22⋊A4 | 3 |
| C3×A4×3−1+2 | 4 |