Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. #20293110 | C2 | semidirect |
| 3. #20292633 | C2 | semidirect |
| 4. #20292629 | C2 | semidirect |
| 5. #20292624 | C2 | semidirect |
| 6. C2×#16812031 | C2 | semidirect |
| 7. C2×#131×C107 | C2 | semidirect |
| 9. #16812155 | C4 | semidirect |
| 16. #16812068 | C22 | semidirect |
| 17. C2×C4⋊Dic107 | C22 | semidirect |
| 18. #16812034 | C22 | semidirect |
| 19. #16812034 | C22 | semidirect |
| 20. #16812031 | C22 | semidirect |
| 21. #16812031 | C22 | semidirect |
| 22. #16812031 | C22 | semidirect |
| 25. C2×M16×C107 | C22 | semidirect |
| 26. C22×C8×C107 | C22 | semidirect |
| 30. #13133818 | C2×C4 | semidirect |
| 34. C2×D428 | C2×C4 | semidirect |
| 98. C107 | #2897 | semidirect |
| 100. C2×#131 | D107 | semidirect |
| 114. C2×M16 | C2×D107 | semidirect |
| 115. C22×C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812155 | 2 |
| #20293110 | 2 |
| #20292633 | 2 |
| #20292629 | 2 |
| #20292624 | 2 |
| C2×#16812031 | 2 |
| C2×#131×C107 | 2 |
| #2897 | 107 |