Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#16812142 | C2 | semidirect |
| 3. C2×#16812097 | C2 | semidirect |
| 4. C4×#13133818 | C2 | semidirect |
| 5. #20292850 | C2 | semidirect |
| 6. #20292843 | C2 | semidirect |
| 7. #20292637 | C2 | semidirect |
| 8. #20292633 | C2 | semidirect |
| 9. #423×C107 | C2 | semidirect |
| 15. C2×Dic428 | C22 | semidirect |
| 17. C2×#13133807 | C22 | semidirect |
| 22. C4×Dic214 | C22 | semidirect |
| 23. C4×D428 | C22 | semidirect |
| 29. #16812034 | C22 | semidirect |
| 34. C4⋊C8×C107 | C22 | semidirect |
| 126. C107 | #3040 | semidirect |
| 133. #423 | D107 | semidirect |
| 158. C4⋊C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812142 | 2 |
| C2×#16812137 | 2 |
| C2×#16812097 | 2 |
| C4×#13133818 | 2 |
| #20292850 | 2 |
| #20292843 | 2 |
| #20292637 | 2 |
| #20292633 | 2 |
| #423×C107 | 2 |
| #3040 | 107 |