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. #20293177 | C2 | semidirect |
| 2. C2×C4×D428 | C2 | semidirect |
| 3. #20292941 | C2 | semidirect |
| 4. #20292908 | C2 | semidirect |
| 5. #20292823 | C2 | semidirect |
| 6. #20292763 | C2 | semidirect |
| 7. C4×D856 | C2 | semidirect |
| 8. #431×C107 | C2 | semidirect |
| 13. #16812109 | C22 | semidirect |
| 14. #16812106 | C22 | semidirect |
| 23. C4×D428 | C22 | semidirect |
| 26. #16812043 | C22 | semidirect |
| 28. #16812031 | C22 | semidirect |
| 30. C4⋊C8×C107 | C22 | semidirect |
| 32. C4×C8×C107 | C22 | semidirect |
| 73. C2×C4×C107 | D8 | semidirect |
| 89. D428 | #41 | semidirect |
| 121. C107 | #3100 | semidirect |
| 129. #431 | D107 | semidirect |
| 149. C4⋊C8 | C2×D107 | semidirect |
| 153. C4×C8 | C2×D107 | semidirect |
| 208. C2×C4 | D856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293177 | 2 |
| C2×C4×D428 | 2 |
| #20292941 | 2 |
| #20292908 | 2 |
| #20292823 | 2 |
| #20292763 | 2 |
| C4×D856 | 2 |
| #431×C107 | 2 |
| #3100 | 107 |