Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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. Q32×D107 | C2 | semidirect |
| 3. #20292467 | C2 | semidirect |
| 4. #20292466 | C2 | semidirect |
| 5. #20292464 | C2 | semidirect |
| 6. #20292460 | C2 | semidirect |
| 7. Q64×C107 | C2 | semidirect |
| 52. C107 | #2264 | semidirect |
| 56. Q64 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293060 | 2 |
| Q32×D107 | 2 |
| #20292467 | 2 |
| #20292466 | 2 |
| #20292464 | 2 |
| #20292460 | 2 |
| Q64×C107 | 2 |
| #2264 | 107 |