Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1178 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 454 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. H(3,𝔽3)×#4294 | C3 | semidirect |
| 3. C9×C32⋊(C19⋊C3) | C3 | semidirect |
| 4. #17987406 | C3 | semidirect |
| 5. C3×#13095303 | C3 | semidirect |
| 6. C19⋊C3×C32⋊C9 | C3 | semidirect |
| 7. C9×C19×H(3,𝔽3) | C3 | semidirect |
| 10. H(3,𝔽3)×C19⋊C3 | C9 | semidirect |
| 11. C32×#4294 | C32 | semidirect |
| 12. C3×C9×C19⋊C3 | C32 | semidirect |
| 13. C32⋊#4294 | C32 | semidirect |
| 16. #13095303 | C32 | semidirect |
| 17. #13095303 | C32 | semidirect |
| 18. #13095303 | C32 | semidirect |
| 20. C32×C9×C19 | C32 | semidirect |
| 21. C19×C32⋊C9 | C32 | semidirect |
| 27. C32×C19⋊C3 | C3×C9 | semidirect |
| 30. C19×H(3,𝔽3) | C3×C9 | semidirect |
| 34. C32⋊(C19⋊C3) | C3×C9 | semidirect |
| 43. C9×H(3,𝔽3) | C19⋊C3 | semidirect |
| 70. C32×C9 | C3×C19⋊C3 | semidirect |
| 77. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 93. H(3,𝔽3) | C9×C19⋊C3 | semidirect |
| 101. C19 | #10624862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(3,𝔽3)×C19⋊C3 | 3 |
| H(3,𝔽3)×#4294 | 3 |
| C9×C32⋊(C19⋊C3) | 3 |
| #17987406 | 3 |
| C3×#13095303 | 3 |
| C19⋊C3×C32⋊C9 | 3 |
| C9×C19×H(3,𝔽3) | 3 |
| #10624862 | 19 |