Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 2. C2×#16812116 | C2 | semidirect |
| 3. #20293198 | C2 | semidirect |
| 4. #20292883 | C2 | semidirect |
| 5. #20292871 | C2 | semidirect |
| 6. #20292866 | C2 | semidirect |
| 7. #20292854 | C2 | semidirect |
| 8. #20292667 | C2 | semidirect |
| 9. #20292623 | C2 | semidirect |
| 10. C2×#16812032 | C2 | semidirect |
| 51. #13133802 | D4 | semidirect |
| 144. C107 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812139 | 2 |
| C2×#16812116 | 2 |
| #20293198 | 2 |
| #20292883 | 2 |
| #20292871 | 2 |
| #20292866 | 2 |
| #20292854 | 2 |
| #20292667 | 2 |
| #20292623 | 2 |
| C2×#16812032 | 2 |
| #537×C107 | 2 |
| #3063 | 107 |