Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 3. C2×#16812097 | C2 | semidirect |
| 4. #20292849 | C2 | semidirect |
| 5. #20292842 | C2 | semidirect |
| 6. #20292651 | C2 | semidirect |
| 7. #20292635 | C2 | semidirect |
| 8. #20292631 | C2 | semidirect |
| 9. C4×#41×C107 | C2 | semidirect |
| 14. C2×#13133808 | C22 | semidirect |
| 15. C2×#13133806 | C22 | semidirect |
| 24. C4⋊(C107⋊C8) | C22 | semidirect |
| 25. #16812032 | C22 | semidirect |
| 28. C4×Q8×C107 | C22 | semidirect |
| 30. C4×D4×C107 | C22 | semidirect |
| 126. C107 | #3040 | semidirect |
| 130. C4×#41 | D107 | semidirect |
| 150. C4×Q8 | C2×D107 | semidirect |
| 152. C4×D4 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812139 | 2 |
| C2×#16812134 | 2 |
| C2×#16812097 | 2 |
| #20292849 | 2 |
| #20292842 | 2 |
| #20292651 | 2 |
| #20292635 | 2 |
| #20292631 | 2 |
| C4×#41×C107 | 2 |
| #3040 | 107 |