Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #20293177 | C2 | semidirect |
| 2. #20293037 | C2 | semidirect |
| 3. #20293017 | C2 | semidirect |
| 4. #20292993 | C2 | semidirect |
| 5. #20292986 | C2 | semidirect |
| 6. #20292878 | C2 | semidirect |
| 7. #20292875 | C2 | semidirect |
| 8. C4×#13133805 | C2 | semidirect |
| 9. C4×#13133803 | C2 | semidirect |
| 10. C4×#13133802 | C2 | semidirect |
| 11. #529×C107 | C2 | semidirect |
| 110. C107⋊C8 | #41 | semidirect |
| 138. C107 | #3171 | semidirect |
| 140. #529 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293177 | 2 |
| #20293037 | 2 |
| #20293017 | 2 |
| #20292993 | 2 |
| #20292986 | 2 |
| #20292878 | 2 |
| #20292875 | 2 |
| C4×#13133805 | 2 |
| C4×#13133803 | 2 |
| C4×#13133802 | 2 |
| #529×C107 | 2 |
| #3171 | 107 |