Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
616 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 173 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×#13133803 | C2 | semidirect |
| 2. C23×C107⋊C8 | C2 | semidirect |
| 3. C2×#16812083 | C2 | semidirect |
| 4. #20292861 | C2 | direct (N × H) |
| 5. C2×#16812042 | C2 | semidirect |
| 6. C2×#16812030 | C2 | semidirect |
| 7. C2×#16812029 | C2 | semidirect |
| 8. C2×#121×C107 | C2 | semidirect |
| 12. C2×#13133803 | C22 | semidirect |
| 16. C22×C107⋊C8 | C22 | semidirect |
| 18. #16812083 | C22 | semidirect |
| 21. #16812042 | C22 | semidirect |
| 22. #16812030 | C22 | semidirect |
| 23. #16812029 | C22 | semidirect |
| 28. #121×C107 | C22 | semidirect |
| 42. C2×C107⋊C8 | D4 | semidirect |
| 72. C23×C107 | D8 | semidirect |
| 101. C107⋊C8 | C2×D4 | semidirect |
| 111. C22×C107 | C2×D8 | semidirect |
| 126. C2×C107 | #466 | semidirect |
| 132. C107 | C2×#466 | semidirect |
| 136. C2×#121 | D107 | semidirect |
| 155. #121 | C2×D107 | semidirect |
| 208. C23 | #13133803 | semidirect |
| 247. C22 | C2×#13133803 | semidirect |
| 259. C2 | #20292861 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133803 | 2 |
| C23×C107⋊C8 | 2 |
| C2×#16812083 | 2 |
| #20292861 | 2 |
| C2×#16812042 | 2 |
| C2×#16812030 | 2 |
| C2×#16812029 | 2 |
| C2×#121×C107 | 2 |
| C2×#466 | 107 |