Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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 |
|---|---|---|
| 1. C2×#16812134 | C2 | semidirect |
| 2. C2×#16812115 | C2 | semidirect |
| 3. #20293205 | C2 | semidirect |
| 4. #20293196 | C2 | semidirect |
| 5. #20292879 | C2 | semidirect |
| 6. #20292876 | C2 | semidirect |
| 7. #20292862 | C2 | semidirect |
| 8. #20292859 | C2 | semidirect |
| 9. #20292670 | C2 | semidirect |
| 10. C2×#16812031 | C2 | semidirect |
| 11. #416×C107 | C2 | semidirect |
| 19. C2×#13133801 | C22 | semidirect |
| 20. C2×C8×D107 | C22 | semidirect |
| 24. #16812085 | C22 | semidirect |
| 29. #16812080 | C22 | semidirect |
| 32. #16812042 | C22 | semidirect |
| 33. #16812040 | C22 | semidirect |
| 39. #103×C107 | C22 | semidirect |
| 40. #103×C107 | C22 | semidirect |
| 41. #102×C107 | C22 | semidirect |
| 42. #102×C107 | C22 | semidirect |
| 60. #13133802 | D4 | semidirect |
| 152. C107 | #3062 | semidirect |
| 162. #416 | D107 | semidirect |
| 189. #103 | C2×D107 | semidirect |
| 190. #103 | C2×D107 | semidirect |
| 193. #102 | C2×D107 | semidirect |
| 194. #102 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812134 | 2 |
| C2×#16812115 | 2 |
| #20293205 | 2 |
| #20293196 | 2 |
| #20292879 | 2 |
| #20292876 | 2 |
| #20292862 | 2 |
| #20292859 | 2 |
| #20292670 | 2 |
| C2×#16812031 | 2 |
| #416×C107 | 2 |
| #3062 | 107 |