Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. C2×#16812131 | C2 | semidirect |
| 2. C2×#16812128 | C2 | semidirect |
| 3. #20293295 | C2 | semidirect |
| 4. #20293002 | C2 | semidirect |
| 5. #20292864 | C2 | semidirect |
| 6. #20292826 | C2 | semidirect |
| 7. #20292773 | C2 | semidirect |
| 8. #20292770 | C2 | semidirect |
| 9. #20292721 | C2 | semidirect |
| 10. C8×C22⋊D107 | C2 | semidirect |
| 11. #466×C107 | C2 | semidirect |
| 56. Dic428 | D4 | semidirect |
| 134. Dic107 | #135 | semidirect |
| 143. C107 | #3287 | semidirect |
| 149. #466 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| C2×#16812128 | 2 |
| #20293295 | 2 |
| #20293002 | 2 |
| #20292864 | 2 |
| #20292826 | 2 |
| #20292773 | 2 |
| #20292770 | 2 |
| #20292721 | 2 |
| C8×C22⋊D107 | 2 |
| #466×C107 | 2 |
| #3287 | 107 |