Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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×C4×D428 | C2 | semidirect |
| 2. #20292938 | C2 | semidirect |
| 3. #20292904 | C2 | semidirect |
| 4. #20292819 | C2 | semidirect |
| 5. #20292760 | C2 | semidirect |
| 6. C4×#13133803 | C2 | semidirect |
| 7. #20292680 | C2 | semidirect |
| 8. #532×C107 | C2 | semidirect |
| 18. #16812042 | C22 | semidirect |
| 19. C4⋊(C107⋊C8) | C22 | semidirect |
| 20. #16812030 | C22 | semidirect |
| 23. C4×C107⋊C8 | C22 | semidirect |
| 25. C4⋊Q8×C107 | C22 | semidirect |
| 26. #127×C107 | C22 | semidirect |
| 31. C4×D4×C107 | C22 | semidirect |
| 80. C2×C4×C107 | D8 | semidirect |
| 91. D428 | #41 | semidirect |
| 121. C107 | #3100 | semidirect |
| 122. #532 | D107 | semidirect |
| 134. C4⋊Q8 | C2×D107 | semidirect |
| 135. #127 | C2×D107 | semidirect |
| 144. C4×D4 | C2×D107 | semidirect |
| 208. C2×C4 | #13133803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D428 | 2 |
| #20292938 | 2 |
| #20292904 | 2 |
| #20292819 | 2 |
| #20292760 | 2 |
| C4×#13133803 | 2 |
| #20292680 | 2 |
| #532×C107 | 2 |
| #3100 | 107 |