Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 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×#16812137 | C2 | semidirect |
| 2. C2×#16812135 | C2 | semidirect |
| 3. C22×#13133803 | C2 | semidirect |
| 4. C2×#16812117 | C2 | semidirect |
| 5. #20292896 | C2 | direct (N × H) |
| 6. C2×#16812044 | C2 | semidirect |
| 7. C2×#16812025 | C2 | semidirect |
| 8. C2×#100×C107 | C2 | semidirect |
| 12. #16812137 | C22 | semidirect |
| 14. #16812135 | C22 | semidirect |
| 22. C2×#13133803 | C22 | semidirect |
| 24. #16812117 | C22 | semidirect |
| 29. #16812044 | C22 | semidirect |
| 30. #16812025 | C22 | semidirect |
| 34. #100×C107 | C22 | semidirect |
| 139. C2×C107 | #472 | semidirect |
| 144. C107 | C2×#472 | semidirect |
| 152. C2×#100 | D107 | semidirect |
| 178. #100 | C2×D107 | semidirect |
| 285. C2 | #20292896 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812137 | 2 |
| C2×#16812135 | 2 |
| C22×#13133803 | 2 |
| C2×#16812117 | 2 |
| #20292896 | 2 |
| C2×#16812044 | 2 |
| C2×#16812025 | 2 |
| C2×#100×C107 | 2 |
| C2×#472 | 107 |