Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
476 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 108 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. #17987560 | C3 | direct (N × H) |
| 8. C32×#4294 | C9 | semidirect |
| 13. C3×C9×C19⋊C3 | C9 | semidirect |
| 15. C32×C9×C19 | C9 | semidirect |
| 30. C3×C9×C19 | C3×C9 | semidirect |
| 33. C3×#4294 | C3×C9 | semidirect |
| 70. C32×C9 | #4296 | semidirect |
| 75. C3×C19 | #6868 | semidirect |
| 79. C19⋊C3 | #6868 | semidirect |
| 102. C3×C9 | C3×#4296 | semidirect |
| 103. C19 | C3×#6868 | semidirect |
| 131. C3 | #17987560 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊#4296 | 3 |
| #17987560 | 3 |
| C32×C9×C19⋊C3 | 3 |
| C3×#6868 | 19 |