Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #20293101 | C2 | semidirect |
| 3. #20292738 | C2 | semidirect |
| 4. #20292709 | C2 | semidirect |
| 5. #20292631 | C2 | semidirect |
| 6. #20292582 | C2 | semidirect |
| 7. #427×C107 | C2 | semidirect |
| 9. C2×D856 | C4 | semidirect |
| 14. #16812071 | C22 | semidirect |
| 17. #16812029 | C22 | semidirect |
| 18. #16812019 | C22 | semidirect |
| 19. C8×Dic107 | C22 | semidirect |
| 22. #107×C107 | C22 | semidirect |
| 23. #106×C107 | C22 | semidirect |
| 27. C2×D428 | C2×C4 | semidirect |
| 30. D856 | C2×C4 | semidirect |
| 31. D856 | C2×C4 | semidirect |
| 39. C2×C8×C107 | C2×C4 | semidirect |
| 78. C107 | #2948 | semidirect |
| 83. #427 | D107 | semidirect |
| 97. #107 | C2×D107 | semidirect |
| 98. #106 | C2×D107 | semidirect |
| 113. C2×C8 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D856 | 2 |
| #20293101 | 2 |
| #20292738 | 2 |
| #20292709 | 2 |
| #20292631 | 2 |
| #20292582 | 2 |
| #427×C107 | 2 |
| #2948 | 107 |