Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#16812134 | C2 | semidirect |
| 2. C22×D856 | C2 | semidirect |
| 3. #20293191 | C2 | semidirect |
| 4. #20293101 | C2 | semidirect |
| 5. #20292845 | C2 | semidirect |
| 6. #20292821 | C2 | semidirect |
| 7. #20292653 | C2 | semidirect |
| 8. #20292631 | C2 | semidirect |
| 9. #416×C107 | C2 | semidirect |
| 13. C2×#13133805 | C22 | semidirect |
| 16. C2×#13133803 | C22 | semidirect |
| 18. #16812105 | C22 | semidirect |
| 19. #16812098 | C22 | semidirect |
| 23. #16812071 | C22 | semidirect |
| 26. Dic107⋊C8 | C22 | semidirect |
| 27. #16812029 | C22 | semidirect |
| 31. #103×C107 | C22 | semidirect |
| 32. #102×C107 | C22 | semidirect |
| 40. C2×D428 | D4 | semidirect |
| 122. C107 | #3041 | semidirect |
| 131. #416 | D107 | semidirect |
| 152. #103 | C2×D107 | semidirect |
| 154. #102 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812134 | 2 |
| C22×D856 | 2 |
| #20293191 | 2 |
| #20293101 | 2 |
| #20292845 | 2 |
| #20292821 | 2 |
| #20292653 | 2 |
| #20292631 | 2 |
| #416×C107 | 2 |
| #3041 | 107 |