Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 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. #20293101 | C2 | semidirect |
| 3. #20292740 | C2 | semidirect |
| 4. C4×D856 | C2 | semidirect |
| 5. #20292665 | C2 | semidirect |
| 6. #20292633 | C2 | semidirect |
| 7. #405×C107 | C2 | semidirect |
| 9. C2×D856 | C4 | semidirect |
| 12. C4×D428 | C22 | semidirect |
| 16. #16812043 | C22 | semidirect |
| 17. #16812041 | C22 | semidirect |
| 18. #16812031 | C22 | semidirect |
| 22. #97×C107 | C22 | semidirect |
| 23. C4×C8×C107 | C22 | semidirect |
| 27. C2×D428 | C2×C4 | semidirect |
| 30. D856 | C2×C4 | semidirect |
| 31. D856 | C2×C4 | semidirect |
| 38. C2×C8×C107 | C2×C4 | semidirect |
| 78. C107 | #2948 | semidirect |
| 85. #405 | D107 | semidirect |
| 100. #97 | C2×D107 | semidirect |
| 101. C4×C8 | C2×D107 | semidirect |
| 112. 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 |
| #20292740 | 2 |
| C4×D856 | 2 |
| #20292665 | 2 |
| #20292633 | 2 |
| #405×C107 | 2 |
| #2948 | 107 |