Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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. #20293393 | C2 | semidirect |
| 3. #20292748 | C2 | semidirect |
| 4. #20292743 | C2 | semidirect |
| 5. C2×#16812035 | C2 | semidirect |
| 6. M16×Dic107 | C2 | semidirect |
| 7. #430×C107 | C2 | semidirect |
| 9. #16812142 | C4 | semidirect |
| 10. #16812137 | C4 | semidirect |
| 12. #16812117 | C22 | semidirect |
| 17. #16812035 | C22 | semidirect |
| 18. #16812035 | C22 | semidirect |
| 19. #16812019 | C22 | semidirect |
| 20. C8×Dic107 | C22 | semidirect |
| 23. #108×C107 | C22 | semidirect |
| 33. Dic428 | C2×C4 | semidirect |
| 34. #13133807 | C2×C4 | semidirect |
| 35. D856 | C2×C4 | semidirect |
| 86. C107 | #2956 | semidirect |
| 91. #430 | D107 | semidirect |
| 105. #108 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293427 | 2 |
| #20293393 | 2 |
| #20292748 | 2 |
| #20292743 | 2 |
| C2×#16812035 | 2 |
| M16×Dic107 | 2 |
| #430×C107 | 2 |
| #2956 | 107 |