Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 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. C2×#16812116 | C2 | semidirect |
| 3. #20292635 | C2 | semidirect |
| 4. #20292626 | C2 | semidirect |
| 5. #20292621 | C2 | semidirect |
| 6. C2×#16812032 | C2 | semidirect |
| 7. #520×C107 | C2 | semidirect |
| 9. #16812156 | C4 | semidirect |
| 28. #13133818 | C2×C4 | semidirect |
| 32. C2×Dic214 | C2×C4 | semidirect |
| 95. C107 | #2898 | semidirect |
| 98. #520 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812156 | 2 |
| C2×#16812116 | 2 |
| #20292635 | 2 |
| #20292626 | 2 |
| #20292621 | 2 |
| C2×#16812032 | 2 |
| #520×C107 | 2 |
| #2898 | 107 |