Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
668 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 55 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. C3×H(3,𝔽3)×C19⋊C3 | C3 | semidirect |
| 2. #17987420 | C3 | semidirect |
| 3. #17987419 | C3 | semidirect |
| 4. #17987310 | C3 | semidirect |
| 5. #17987310 | C3 | semidirect |
| 6. #17987309 | C3 | semidirect |
| 7. C19×#6856 | C3 | semidirect |
| 14. C3×C32⋊(C19⋊C3) | C32 | semidirect |
| 16. C32⋊#4294 | C32 | semidirect |
| 17. C32⋊#4294 | C32 | semidirect |
| 20. C3×C19×H(3,𝔽3) | C32 | semidirect |
| 21. C19×C32⋊C9 | C32 | semidirect |
| 22. C19×C32⋊C9 | C32 | semidirect |
| 52. #6856 | C19⋊C3 | semidirect |
| 86. C3×H(3,𝔽3) | C3×C19⋊C3 | semidirect |
| 91. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 92. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 123. C19 | #10624589 | 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 |
| #17987420 | 3 |
| #17987419 | 3 |
| #17987310 | 3 |
| #17987309 | 3 |
| C19×#6856 | 3 |
| #10624589 | 19 |