Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 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. C2×#16812135 | C2 | semidirect |
| 2. #20293177 | C2 | semidirect |
| 3. #20293014 | C2 | semidirect |
| 4. #20293003 | C2 | semidirect |
| 5. #20292999 | C2 | semidirect |
| 6. C4×#13133802 | C2 | semidirect |
| 7. C2×#127×C107 | C2 | semidirect |
| 10. C2×#13133806 | C22 | semidirect |
| 11. C2×#13133803 | C22 | semidirect |
| 13. #16812109 | C22 | semidirect |
| 14. #16812106 | C22 | semidirect |
| 15. #16812097 | C22 | semidirect |
| 18. #16812020 | C22 | semidirect |
| 19. C4×C107⋊C8 | C22 | semidirect |
| 34. #13133802 | D4 | semidirect |
| 71. C107⋊C8 | C2×D4 | semidirect |
| 82. C4×C107 | AGL(1,ℤ/8) | semidirect |
| 91. C107 | #3151 | semidirect |
| 94. C2×#127 | D107 | semidirect |
| 174. C4 | #16812135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812135 | 2 |
| #20293177 | 2 |
| #20293014 | 2 |
| #20293003 | 2 |
| #20292999 | 2 |
| C4×#13133802 | 2 |
| C2×#127×C107 | 2 |
| #3151 | 107 |