Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13133806 | C2 | semidirect |
| 2. C2×#16812096 | C2 | semidirect |
| 3. C2×D4×Dic107 | C2 | semidirect |
| 4. #20292840 | C2 | direct (N × H) |
| 5. C2×Dic107⋊C8 | C2 | semidirect |
| 6. C2×#16812034 | C2 | semidirect |
| 7. C2×#16812030 | C2 | semidirect |
| 12. C2×#13133806 | C22 | semidirect |
| 15. #16812096 | C22 | semidirect |
| 17. D4×Dic107 | C22 | semidirect |
| 23. Dic107⋊C8 | C22 | semidirect |
| 24. #16812034 | C22 | semidirect |
| 25. #16812030 | C22 | semidirect |
| 119. C2×C107 | #463 | semidirect |
| 124. C107 | C2×#463 | semidirect |
| 243. C2 | #20292840 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133806 | 2 |
| C2×#16812096 | 2 |
| C2×D4×Dic107 | 2 |
| #20292840 | 2 |
| C2×Dic107⋊C8 | 2 |
| C2×#16812034 | 2 |
| C2×#16812030 | 2 |
| C22×D8×C107 | 2 |
| C2×#463 | 107 |