Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
456 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 61 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. C19⋊H(5,𝔽3) | C3 | semidirect |
| 2. #17987509 | C3 | semidirect |
| 3. #17987506 | C3 | semidirect |
| 4. #17987506 | C3 | semidirect |
| 5. #17987506 | C3 | semidirect |
| 6. C3×#13095319 | C3 | semidirect |
| 7. C3×#13095318 | C3 | semidirect |
| 8. #17987432 | C3 | semidirect |
| 9. C19×#6910 | C3 | semidirect |
| 10. C3×#10587025 | C32 | semidirect |
| 11. C3×#10587025 | C32 | semidirect |
| 15. C3×C32⋊(C19⋊C3) | C32 | semidirect |
| 18. C32×#4294 | C32 | semidirect |
| 26. C3×C19×3−1+2 | C32 | semidirect |
| 27. C3×C19×3−1+2 | C32 | semidirect |
| 67. #6910 | C19⋊C3 | semidirect |
| 94. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 95. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 154. C19 | #10624748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19⋊H(5,𝔽3) | 3 |
| #17987509 | 3 |
| #17987506 | 3 |
| C3×#13095319 | 3 |
| C3×#13095318 | 3 |
| #17987432 | 3 |
| C19×#6910 | 3 |
| #10624748 | 19 |