Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20292968 | C2 | semidirect |
| 3. #20292962 | C2 | semidirect |
| 4. #20292951 | C2 | semidirect |
| 5. #20292940 | C2 | semidirect |
| 6. #20292670 | C2 | semidirect |
| 7. C2×#16812042 | C2 | semidirect |
| 8. #20292626 | C2 | semidirect |
| 9. #20292621 | C2 | semidirect |
| 10. #20292594 | C2 | semidirect |
| 11. #520×C107 | C2 | semidirect |
| 134. C107 | #3098 | semidirect |
| 136. #520 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293205 | 2 |
| #20292968 | 2 |
| #20292962 | 2 |
| #20292951 | 2 |
| #20292940 | 2 |
| #20292670 | 2 |
| C2×#16812042 | 2 |
| #20292626 | 2 |
| #20292621 | 2 |
| #20292594 | 2 |
| #520×C107 | 2 |
| #3098 | 107 |