Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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. #20292668 | C2 | semidirect |
| 4. #20292666 | C2 | semidirect |
| 5. #20292665 | C2 | semidirect |
| 6. #20292663 | C2 | semidirect |
| 7. #427×C107 | C2 | semidirect |
| 9. C2×#13133801 | C4 | semidirect |
| 20. #16812043 | C22 | semidirect |
| 21. #16812042 | C22 | semidirect |
| 22. #16812041 | C22 | semidirect |
| 23. #16812040 | C22 | semidirect |
| 26. #107×C107 | C22 | semidirect |
| 27. #106×C107 | C22 | semidirect |
| 35. #13133801 | C2×C4 | semidirect |
| 36. #13133801 | C2×C4 | semidirect |
| 37. C2×C107⋊C8 | C2×C4 | semidirect |
| 46. C2×C8×C107 | C2×C4 | semidirect |
| 88. C107 | #2911 | semidirect |
| 95. #427 | D107 | semidirect |
| 112. #107 | C2×D107 | semidirect |
| 115. #106 | C2×D107 | semidirect |
| 128. 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×#13133801 | 2 |
| #117×D107 | 2 |
| #20292668 | 2 |
| #20292666 | 2 |
| #20292665 | 2 |
| #20292663 | 2 |
| #427×C107 | 2 |
| #2911 | 107 |