Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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×#16812116 | C2 | semidirect |
| 2. #20293110 | C2 | semidirect |
| 3. #20292632 | C2 | semidirect |
| 4. #20292628 | C2 | semidirect |
| 5. #20292623 | C2 | semidirect |
| 6. C2×#16812030 | C2 | semidirect |
| 9. C2×#13133802 | C22 | semidirect |
| 10. C22×C107⋊C8 | C22 | semidirect |
| 13. #16812068 | C22 | semidirect |
| 14. C2×C4⋊Dic107 | C22 | semidirect |
| 15. #16812033 | C22 | semidirect |
| 16. #16812033 | C22 | semidirect |
| 17. #16812030 | C22 | semidirect |
| 18. #16812030 | C22 | semidirect |
| 19. #16812030 | C22 | semidirect |
| 21. H(5,𝔽2)×C107 | C4 | semidirect |
| 41. #41×C107 | C2×C4 | semidirect |
| 49. C2×D4×C107 | C2×C4 | semidirect |
| 98. C107 | #2897 | semidirect |
| 107. H(5,𝔽2) | Dic107 | semidirect |
| 129. #41 | C2×Dic107 | semidirect |
| 137. C2×D4 | C2×Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812116 | 2 |
| #20293110 | 2 |
| #20292632 | 2 |
| #20292628 | 2 |
| #20292623 | 2 |
| C2×#16812030 | 2 |
| C2×H(5,𝔽2)×C107 | 2 |
| #2897 | 107 |