Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20293104 | C2 | semidirect |
| 3. #20292727 | C2 | semidirect |
| 4. C4×#13133806 | C2 | semidirect |
| 5. #20292663 | C2 | semidirect |
| 6. #20292635 | C2 | semidirect |
| 8. #20292583 | C2 | semidirect |
| 11. C2×#13133806 | C4 | semidirect |
| 16. C4×Dic214 | C22 | semidirect |
| 20. #16812042 | C22 | semidirect |
| 21. #16812040 | C22 | semidirect |
| 22. #16812032 | C22 | semidirect |
| 24. #16812020 | C22 | semidirect |
| 25. C4×C107⋊C8 | C22 | semidirect |
| 34. C2×Dic214 | C2×C4 | semidirect |
| 37. #13133806 | C2×C4 | semidirect |
| 38. #13133806 | C2×C4 | semidirect |
| 40. C2×C107⋊C8 | C2×C4 | semidirect |
| 104. C107 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133806 | 2 |
| #20293104 | 2 |
| #20292727 | 2 |
| C4×#13133806 | 2 |
| #20292663 | 2 |
| #20292635 | 2 |
| #20292632 | 2 |
| #20292583 | 2 |
| #518×C107 | 2 |
| #2949 | 107 |