Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 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. #20292978 | C2 | semidirect |
| 4. #20292964 | C2 | semidirect |
| 5. #20292922 | C2 | semidirect |
| 6. #20292867 | C2 | semidirect |
| 7. #20292837 | C2 | semidirect |
| 8. #20292781 | C2 | semidirect |
| 10. #103×D107 | C2 | semidirect |
| 11. C4×Q16×C107 | C2 | semidirect |
| 91. D428 | Q16 | semidirect |
| 123. C107 | #3299 | semidirect |
| 132. C4×Q16 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293337 | 2 |
| Q8×D428 | 2 |
| #20292978 | 2 |
| #20292964 | 2 |
| #20292922 | 2 |
| #20292867 | 2 |
| #20292837 | 2 |
| #20292781 | 2 |
| C8×D428 | 2 |
| #103×D107 | 2 |
| C4×Q16×C107 | 2 |
| #3299 | 107 |