Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #20292965 | C2 | semidirect |
| 3. #20292919 | C2 | semidirect |
| 4. #20292914 | C2 | semidirect |
| 5. #20292834 | C2 | semidirect |
| 6. #20292829 | C2 | semidirect |
| 8. #20292732 | C2 | semidirect |
| 9. #20292725 | C2 | semidirect |
| 10. #20292684 | C2 | semidirect |
| 11. #533×C107 | C2 | semidirect |
| 137. C107 | #3116 | semidirect |
| 138. #533 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133818 | 2 |
| #20292965 | 2 |
| #20292919 | 2 |
| #20292914 | 2 |
| #20292834 | 2 |
| #20292829 | 2 |
| #20292787 | 2 |
| #20292732 | 2 |
| #20292725 | 2 |
| #20292684 | 2 |
| #533×C107 | 2 |
| #3116 | 107 |