Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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. #20292527 | C2 | semidirect |
| 3. #20292521 | C2 | semidirect |
| 4. #20292515 | C2 | semidirect |
| 5. #20292503 | C2 | semidirect |
| 6. #20292483 | C2 | semidirect |
| 7. #379×C107 | C2 | semidirect |
| 9. C22×C4×D107 | C22 | semidirect |
| 10. #16812078 | C4 | semidirect |
| 11. C2×Dic107⋊C4 | C22 | semidirect |
| 15. C2×(C2×D107)⋊C4 | C22 | semidirect |
| 16. C2×C4×Dic107 | C22 | semidirect |
| 17. C107⋊#95 | C22 | semidirect |
| 18. C107⋊#95 | C22 | semidirect |
| 33. C22⋊Dic107 | C2×C4 | semidirect |
| 38. C24×C107 | C2×C4 | semidirect |
| 96. C107 | #2375 | semidirect |
| 103. #379 | D107 | semidirect |
| 121. C24 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812078 | 2 |
| #20292527 | 2 |
| #20292521 | 2 |
| #20292515 | 2 |
| #20292503 | 2 |
| #20292483 | 2 |
| #379×C107 | 2 |
| #2375 | 107 |