Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#13133803 | C2 | semidirect |
| 2. #20293191 | C2 | semidirect |
| 3. #20293102 | C2 | semidirect |
| 4. #20292844 | C2 | semidirect |
| 5. #20292820 | C2 | semidirect |
| 6. #20292655 | C2 | semidirect |
| 7. #20292633 | C2 | semidirect |
| 8. #20292623 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C107 | C2 | semidirect |
| 14. #16812105 | C22 | semidirect |
| 15. #16812098 | C22 | semidirect |
| 19. D4×Dic107 | C22 | semidirect |
| 23. Dic107⋊C8 | C22 | semidirect |
| 24. #16812033 | C22 | semidirect |
| 25. #16812031 | C22 | semidirect |
| 26. #16812030 | C22 | semidirect |
| 30. C2×SD16×C107 | C22 | semidirect |
| 31. C2×D8×C107 | C22 | semidirect |
| 58. C2×D4×C107 | D4 | semidirect |
| 122. C107 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D107 | semidirect |
| 136. C2×SD16 | C2×D107 | semidirect |
| 139. C2×D8 | C2×D107 | semidirect |
| 168. C2×D4 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133803 | 2 |
| #20293191 | 2 |
| #20293102 | 2 |
| #20292844 | 2 |
| #20292820 | 2 |
| #20292655 | 2 |
| #20292633 | 2 |
| #20292623 | 2 |
| C2×AGL(1,ℤ/8)×C107 | 2 |
| #3041 | 107 |