Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20293068 | C2 | semidirect |
| 3. #20293067 | C2 | semidirect |
| 4. #20293063 | C2 | semidirect |
| 5. #20293062 | C2 | semidirect |
| 6. #20293057 | C2 | semidirect |
| 7. C2×#16812049 | C2 | semidirect |
| 8. C2×#135×C107 | C2 | semidirect |
| 13. #16812131 | C22 | semidirect |
| 14. C2×Dic428 | C22 | semidirect |
| 16. C2×D856 | C22 | semidirect |
| 17. #16812055 | C22 | semidirect |
| 18. #16812053 | C22 | semidirect |
| 19. #16812052 | C22 | semidirect |
| 20. #16812050 | C22 | semidirect |
| 21. #16812049 | C22 | semidirect |
| 22. #16812049 | C22 | semidirect |
| 23. C2×C107⋊C16 | C22 | semidirect |
| 28. #135×C107 | C22 | semidirect |
| 29. C2×Q16×C107 | C22 | semidirect |
| 31. C2×D8×C107 | C22 | semidirect |
| 121. C107 | #3414 | semidirect |
| 123. C2×#135 | D107 | semidirect |
| 139. #135 | C2×D107 | semidirect |
| 141. C2×Q16 | C2×D107 | semidirect |
| 145. C2×D8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| #20293068 | 2 |
| #20293067 | 2 |
| #20293063 | 2 |
| #20293062 | 2 |
| #20293057 | 2 |
| C2×#16812049 | 2 |
| C2×#135×C107 | 2 |
| #3414 | 107 |