Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #20293102 | C2 | semidirect |
| 3. #20293101 | C2 | semidirect |
| 4. #20292736 | C2 | semidirect |
| 5. #20292707 | C2 | semidirect |
| 6. #20292663 | C2 | semidirect |
| 7. #20292633 | C2 | semidirect |
| 8. #20292585 | C2 | semidirect |
| 9. #418×C107 | C2 | semidirect |
| 11. C2×#13133803 | C4 | semidirect |
| 17. D4×Dic107 | C22 | semidirect |
| 18. #16812071 | C22 | semidirect |
| 23. #16812042 | C22 | semidirect |
| 24. #16812040 | C22 | semidirect |
| 25. #16812031 | C22 | semidirect |
| 26. #16812019 | C22 | semidirect |
| 27. C8×Dic107 | C22 | semidirect |
| 31. #102×C107 | C22 | semidirect |
| 35. C2×D428 | C2×C4 | semidirect |
| 39. #13133803 | C2×C4 | semidirect |
| 40. #13133803 | C2×C4 | semidirect |
| 41. C2×C107⋊C8 | C2×C4 | semidirect |
| 55. C2×D4×C107 | C2×C4 | semidirect |
| 109. C107 | #2948 | semidirect |
| 117. #418 | D107 | semidirect |
| 138. #102 | C2×D107 | semidirect |
| 149. C2×D4 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133803 | 2 |
| #20293102 | 2 |
| #20293101 | 2 |
| #20292736 | 2 |
| #20292707 | 2 |
| #20292663 | 2 |
| #20292633 | 2 |
| #20292585 | 2 |
| #418×C107 | 2 |
| #2948 | 107 |