Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
464 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. C2×#16812117 | C2 | semidirect |
| 3. #20292748 | C2 | direct (N × H) |
| 4. C2×#16812035 | C2 | semidirect |
| 5. C2×#16812019 | C2 | semidirect |
| 6. C2×#108×C107 | C2 | semidirect |
| 8. #16812131 | C4 | semidirect |
| 10. C2×Dic428 | C4 | semidirect |
| 11. C2×#13133807 | C4 | semidirect |
| 12. C2×D856 | C4 | semidirect |
| 14. #16812117 | C22 | semidirect |
| 19. #16812035 | C22 | semidirect |
| 20. #16812019 | C22 | semidirect |
| 23. #108×C107 | C22 | semidirect |
| 33. Dic428 | C2×C4 | semidirect |
| 34. #13133807 | C2×C4 | semidirect |
| 35. D856 | C2×C4 | semidirect |
| 88. C2×C107 | #444 | semidirect |
| 92. C107 | C2×#444 | semidirect |
| 96. C2×#108 | D107 | semidirect |
| 113. #108 | C2×D107 | semidirect |
| 181. C2 | #20292748 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| C2×#16812117 | 2 |
| #20292748 | 2 |
| C2×#16812035 | 2 |
| C2×#16812019 | 2 |
| C2×#108×C107 | 2 |
| C2×#444 | 107 |