Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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. #20293107 | C2 | semidirect |
| 3. #20292971 | C2 | semidirect |
| 4. #20292964 | C2 | semidirect |
| 5. #20292953 | C2 | semidirect |
| 6. #20292942 | C2 | semidirect |
| 7. C2×#16812042 | C2 | semidirect |
| 8. #20292629 | C2 | semidirect |
| 9. #20292621 | C2 | semidirect |
| 10. #20292595 | C2 | semidirect |
| 11. #428×C107 | C2 | semidirect |
| 134. C107 | #3098 | semidirect |
| 141. #428 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293208 | 2 |
| #20293107 | 2 |
| #20292971 | 2 |
| #20292964 | 2 |
| #20292953 | 2 |
| #20292942 | 2 |
| C2×#16812042 | 2 |
| #20292629 | 2 |
| #20292621 | 2 |
| #20292595 | 2 |
| #428×C107 | 2 |
| #3098 | 107 |