Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1088 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 292 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. C32×#10587025 | C3 | semidirect |
| 2. C32×#10587025 | C3 | semidirect |
| 4. #17987511 | C3 | direct (N × H) |
| 5. C3×#13095318 | C3 | semidirect |
| 6. C32×C19×3−1+2 | C3 | semidirect |
| 15. C3×#10587025 | C32 | semidirect |
| 16. C3×#10587025 | C32 | semidirect |
| 17. C3×#10587025 | C32 | semidirect |
| 24. C32×#4294 | C32 | semidirect |
| 25. #13095318 | C32 | semidirect |
| 30. C3×C19×3−1+2 | C32 | semidirect |
| 31. C3×C19×3−1+2 | C32 | semidirect |
| 47. C19×3−1+2 | C33 | semidirect |
| 60. #10587025 | C33 | semidirect |
| 65. C3×#4294 | C33 | semidirect |
| 68. C32×3−1+2 | C19⋊C3 | semidirect |
| 105. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 106. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 121. C3×C19 | #6910 | semidirect |
| 144. 3−1+2 | C32×C19⋊C3 | semidirect |
| 156. C19 | C3×#6910 | semidirect |
| 181. C3 | #17987511 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587025 | 3 |
| C32×C32⋊(C19⋊C3) | 3 |
| #17987511 | 3 |
| C3×#13095318 | 3 |
| C32×C19×3−1+2 | 3 |
| C3×#6910 | 19 |