Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20293107 | C2 | semidirect |
| 3. #20292729 | C2 | semidirect |
| 4. C4×Dic428 | C2 | semidirect |
| 5. C4×D856 | C2 | semidirect |
| 6. C2×#16812043 | C2 | semidirect |
| 7. #20292629 | C2 | semidirect |
| 8. #405×C107 | C2 | semidirect |
| 10. #16812131 | C4 | semidirect |
| 30. #13133818 | C2×C4 | semidirect |
| 37. Dic428 | C2×C4 | semidirect |
| 38. #13133807 | C2×C4 | semidirect |
| 39. D856 | C2×C4 | semidirect |
| 47. C2×C8×C107 | C2×C4 | semidirect |
| 96. C107 | #2951 | semidirect |
| 104. #405 | D107 | semidirect |
| 138. C2×C8 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| #20293107 | 2 |
| #20292729 | 2 |
| C4×Dic428 | 2 |
| C4×D856 | 2 |
| C2×#16812043 | 2 |
| #20292629 | 2 |
| #405×C107 | 2 |
| #2951 | 107 |