Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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. #41×Dic107 | C2 | semidirect |
| 3. #20292643 | C2 | semidirect |
| 4. C2×#16812035 | C2 | semidirect |
| 5. #568×C107 | C2 | semidirect |
| 7. #16812156 | C4 | semidirect |
| 8. #16812155 | C4 | semidirect |
| 14. #16812068 | C22 | semidirect |
| 15. C2×C4×Dic107 | C22 | semidirect |
| 16. #16812035 | C22 | semidirect |
| 17. #16812035 | C22 | semidirect |
| 20. C2×M16×C107 | C22 | semidirect |
| 24. #13133818 | C2×C4 | semidirect |
| 27. C2×Dic214 | C2×C4 | semidirect |
| 29. C2×D428 | C2×C4 | semidirect |
| 84. C107 | #2901 | semidirect |
| 86. #568 | D107 | semidirect |
| 98. C2×M16 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293463 | 2 |
| #41×Dic107 | 2 |
| #20292643 | 2 |
| C2×#16812035 | 2 |
| #568×C107 | 2 |
| #2901 | 107 |