Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #20293025 | C2 | semidirect |
| 4. #20292969 | C2 | semidirect |
| 5. #20292958 | C2 | semidirect |
| 6. #20292923 | C2 | semidirect |
| 7. #20292913 | C2 | semidirect |
| 8. #20292885 | C2 | semidirect |
| 9. C4×Dic428 | C2 | semidirect |
| 10. #20292669 | C2 | semidirect |
| 117. C107 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293347 | 2 |
| #20293334 | 2 |
| #20293025 | 2 |
| #20292969 | 2 |
| #20292958 | 2 |
| #20292923 | 2 |
| #20292913 | 2 |
| #20292885 | 2 |
| C4×Dic428 | 2 |
| #20292669 | 2 |
| #436×C107 | 2 |
| #3356 | 107 |