Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#13133807 | C2 | semidirect |
| 2. #20293198 | C2 | semidirect |
| 4. #20292873 | C2 | semidirect |
| 5. #20292856 | C2 | semidirect |
| 6. #20292665 | C2 | semidirect |
| 7. #20292637 | C2 | semidirect |
| 8. #20292633 | C2 | semidirect |
| 9. C2×#131×C107 | C2 | semidirect |
| 20. #16812088 | C22 | semidirect |
| 25. #16812043 | C22 | semidirect |
| 26. #16812041 | C22 | semidirect |
| 27. #16812034 | C22 | semidirect |
| 32. C2×M16×C107 | C22 | semidirect |
| 34. C22×C8×C107 | C22 | semidirect |
| 67. C2×C8×C107 | D4 | semidirect |
| 121. C107 | #3057 | semidirect |
| 123. C2×#131 | D107 | semidirect |
| 139. C2×M16 | C2×D107 | semidirect |
| 141. C22×C8 | C2×D107 | semidirect |
| 179. C2×C8 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133807 | 2 |
| #20293198 | 2 |
| #20293191 | 2 |
| #20292873 | 2 |
| #20292856 | 2 |
| #20292665 | 2 |
| #20292637 | 2 |
| #20292633 | 2 |
| C2×#131×C107 | 2 |
| #3057 | 107 |