Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 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×#16812129 | C2 | semidirect |
| 2. C2×#16812116 | C2 | semidirect |
| 3. #20293205 | C2 | semidirect |
| 4. #20292875 | C2 | semidirect |
| 5. #20292871 | C2 | semidirect |
| 6. #20292866 | C2 | semidirect |
| 7. #20292861 | C2 | semidirect |
| 8. C2×#16812042 | C2 | semidirect |
| 9. #20292628 | C2 | semidirect |
| 10. #20292626 | C2 | semidirect |
| 11. #537×C107 | C2 | semidirect |
| 58. C2×C107⋊C8 | D4 | semidirect |
| 153. C107 | #3061 | semidirect |
| 157. #537 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812129 | 2 |
| C2×#16812116 | 2 |
| #20293205 | 2 |
| #20292875 | 2 |
| #20292871 | 2 |
| #20292866 | 2 |
| #20292861 | 2 |
| C2×#16812042 | 2 |
| #20292628 | 2 |
| #20292626 | 2 |
| #537×C107 | 2 |
| #3061 | 107 |