Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
2996 conjugacy classes of subgroups; only the 630 normal subgroups are shown.
This group has 2996 conjugacy classes of subgroups — too many to draw. Only its 630 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. C33×#4296 | C3 | semidirect |
| 2. C3×C32⋊#4296 | C3 | direct (N × H) |
| 5. C32×#4296 | C32 | semidirect |
| 6. C32⋊#4296 | C32 | direct (N × H) |
| 9. C33×C19⋊C3 | C9 | semidirect |
| 10. C33×C19⋊C3 | C9 | semidirect |
| 13. C34×C19 | C9 | semidirect |
| 17. C33×C19 | C3×C9 | semidirect |
| 23. C32×C19⋊C3 | C3×C9 | semidirect |
| 24. C32×C19⋊C3 | C3×C9 | semidirect |
| 30. C3×#4296 | C33 | semidirect |
| 35. C32×C19 | C32⋊C9 | semidirect |
| 37. C32×C19 | C32×C9 | semidirect |
| 42. C3×C19⋊C3 | C32⋊C9 | semidirect |
| 44. C3×C19⋊C3 | C32×C9 | semidirect |
| 55. C34 | #4296 | semidirect |
| 60. C3×C19 | C3×C32⋊C9 | semidirect |
| 63. C19⋊C3 | C3×C32⋊C9 | semidirect |
| 79. C33 | C3×#4296 | semidirect |
| 82. C19 | C32×C32⋊C9 | semidirect |
| 94. C32 | C32⋊#4296 | direct (N × H) |
| 96. C32 | C32×#4296 | semidirect |
| 103. C3 | C3×C32⋊#4296 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#4296 | 3 |
| C3×C32⋊#4296 | 3 |
| C34×C19⋊C3 | 3 |
| C32×C32⋊C9 | 19 |