Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×Dic428 | C2 | semidirect |
| 3. C22×#13133806 | C2 | semidirect |
| 4. C2×#16812089 | C2 | semidirect |
| 5. #20292790 | C2 | direct (N × H) |
| 6. C2×#16812032 | C2 | semidirect |
| 7. C2×(C2×D107)⋊C8 | C2 | semidirect |
| 8. C2×#102×C107 | C2 | semidirect |
| 19. C2×Dic428 | C22 | semidirect |
| 21. C2×#13133806 | C22 | semidirect |
| 24. #16812089 | C22 | semidirect |
| 27. #16812032 | C22 | semidirect |
| 28. (C2×D107)⋊C8 | C22 | semidirect |
| 32. #102×C107 | C22 | semidirect |
| 130. C2×C107 | #452 | semidirect |
| 136. C107 | C2×#452 | semidirect |
| 143. C2×#102 | D107 | semidirect |
| 167. #102 | C2×D107 | semidirect |
| 267. C2 | #20292790 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133817 | 2 |
| C22×Dic428 | 2 |
| C22×#13133806 | 2 |
| C2×#16812089 | 2 |
| #20292790 | 2 |
| C2×#16812032 | 2 |
| C2×(C2×D107)⋊C8 | 2 |
| C2×#102×C107 | 2 |
| C2×#452 | 107 |