Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16812117 | C2 | semidirect |
| 3. #20293208 | C2 | semidirect |
| 4. #20293205 | C2 | semidirect |
| 5. #20292884 | C2 | semidirect |
| 6. #20292879 | C2 | semidirect |
| 7. #20292859 | C2 | semidirect |
| 8. #20292855 | C2 | semidirect |
| 9. C2×#16812040 | C2 | semidirect |
| 10. #20292629 | C2 | semidirect |
| 11. #417×C107 | C2 | semidirect |
| 63. C2×C107⋊C8 | D4 | semidirect |
| 153. C107 | #3060 | semidirect |
| 164. #417 | 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×#16812117 | 2 |
| #20293208 | 2 |
| #20293205 | 2 |
| #20292884 | 2 |
| #20292879 | 2 |
| #20292859 | 2 |
| #20292855 | 2 |
| C2×#16812040 | 2 |
| #20292629 | 2 |
| #417×C107 | 2 |
| #3060 | 107 |