Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 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. C2×#16812139 | C2 | semidirect |
| 2. C2×#16812096 | C2 | semidirect |
| 3. #20292805 | C2 | direct (N × H) |
| 4. C2×#16812036 | C2 | semidirect |
| 5. C2×#16812026 | C2 | semidirect |
| 7. C22×Dic214 | C22 | semidirect |
| 9. #16812139 | C22 | semidirect |
| 12. C2×#13133802 | C22 | semidirect |
| 14. #16812096 | C22 | semidirect |
| 16. C2×C4×Dic107 | C22 | semidirect |
| 17. #16812036 | C22 | semidirect |
| 18. #16812026 | C22 | semidirect |
| 30. C2×Dic214 | C23 | semidirect |
| 36. #13133802 | C23 | semidirect |
| 40. C4×Dic107 | C23 | semidirect |
| 117. C2×C107 | #455 | semidirect |
| 120. C107 | C2×#455 | semidirect |
| 237. C2 | #20292805 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812139 | 2 |
| C2×#16812096 | 2 |
| #20292805 | 2 |
| C2×#16812036 | 2 |
| C2×#16812026 | 2 |
| C2×H(5,𝔽2)×C107 | 2 |
| C2×#455 | 107 |