Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16812137 | C2 | semidirect |
| 2. C2×#16812131 | C2 | semidirect |
| 3. #20293196 | C2 | semidirect |
| 4. #20293107 | C2 | semidirect |
| 5. #20292850 | C2 | semidirect |
| 6. #20292843 | C2 | semidirect |
| 7. #20292828 | C2 | semidirect |
| 8. #20292823 | C2 | semidirect |
| 9. #20292629 | C2 | semidirect |
| 10. C2×#16812031 | C2 | semidirect |
| 11. #424×C107 | C2 | semidirect |
| 17. C2×Dic428 | C22 | semidirect |
| 19. C2×#13133807 | C22 | semidirect |
| 20. C2×#13133807 | C22 | semidirect |
| 22. C2×D856 | C22 | semidirect |
| 28. C4×Dic214 | C22 | semidirect |
| 29. C4×D428 | C22 | semidirect |
| 34. #16812034 | C22 | semidirect |
| 37. #16812031 | C22 | semidirect |
| 41. C4⋊C8×C107 | C22 | semidirect |
| 42. C4⋊C8×C107 | C22 | semidirect |
| 47. #13133818 | D4 | semidirect |
| 155. C107 | #3045 | semidirect |
| 164. #424 | D107 | semidirect |
| 192. C4⋊C8 | C2×D107 | semidirect |
| 193. C4⋊C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812137 | 2 |
| C2×#16812131 | 2 |
| #20293196 | 2 |
| #20293107 | 2 |
| #20292850 | 2 |
| #20292843 | 2 |
| #20292828 | 2 |
| #20292823 | 2 |
| #20292629 | 2 |
| C2×#16812031 | 2 |
| #424×C107 | 2 |
| #3045 | 107 |