Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
648 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#16812105 | C2 | semidirect |
| 3. C2×D4×Dic107 | C2 | semidirect |
| 4. #20292820 | C2 | direct (N × H) |
| 5. C2×Dic107⋊C8 | C2 | semidirect |
| 6. C2×#16812031 | C2 | semidirect |
| 7. C2×#16812030 | C2 | semidirect |
| 8. C22×D8×C107 | C2 | semidirect |
| 14. C2×#13133803 | C22 | semidirect |
| 17. #16812105 | C22 | semidirect |
| 19. D4×Dic107 | C22 | semidirect |
| 23. Dic107⋊C8 | C22 | semidirect |
| 24. #16812031 | C22 | semidirect |
| 25. #16812030 | C22 | semidirect |
| 29. C2×D8×C107 | C22 | semidirect |
| 60. C2×D4×C107 | D4 | semidirect |
| 85. D4×C107 | C2×D4 | semidirect |
| 96. C2×Dic107 | D8 | semidirect |
| 125. Dic107 | C2×D8 | semidirect |
| 128. C2×C107 | #459 | semidirect |
| 134. C107 | C2×#459 | semidirect |
| 136. C22×D8 | D107 | semidirect |
| 152. C2×D8 | C2×D107 | semidirect |
| 181. C2×D4 | C22⋊D107 | semidirect |
| 224. D4 | C2×C22⋊D107 | semidirect |
| 263. C2 | #20292820 | 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 |
| C2×#16812105 | 2 |
| C2×D4×Dic107 | 2 |
| #20292820 | 2 |
| C2×Dic107⋊C8 | 2 |
| C2×#16812031 | 2 |
| C2×#16812030 | 2 |
| C22×D8×C107 | 2 |
| C2×#459 | 107 |