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 |
|---|---|---|
| 3. #20292725 | C2 | semidirect |
| 4. C4×#13133805 | C2 | semidirect |
| 5. #20292663 | C2 | semidirect |
| 6. #20292636 | C2 | semidirect |
| 8. #20292583 | C2 | semidirect |
| 9. #519×C107 | C2 | semidirect |
| 11. C2×#13133805 | C4 | semidirect |
| 20. #16812042 | C22 | semidirect |
| 21. #16812040 | C22 | semidirect |
| 22. #16812033 | C22 | semidirect |
| 24. #16812020 | C22 | semidirect |
| 25. C4×C107⋊C8 | C22 | semidirect |
| 28. C4×Q8×C107 | C22 | semidirect |
| 38. #13133805 | C2×C4 | semidirect |
| 39. #13133805 | C2×C4 | semidirect |
| 41. C2×C107⋊C8 | C2×C4 | semidirect |
| 51. C2×Q8×C107 | C2×C4 | semidirect |
| 104. C107 | #2949 | semidirect |
| 106. #519 | D107 | semidirect |
| 122. C4×Q8 | C2×D107 | semidirect |
| 139. C2×Q8 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133805 | 2 |
| #20293101 | 2 |
| #20292725 | 2 |
| C4×#13133805 | 2 |
| #20292663 | 2 |
| #20292636 | 2 |
| #20292631 | 2 |
| #20292583 | 2 |
| #519×C107 | 2 |
| #2949 | 107 |