Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 3. C22×#13133807 | C2 | semidirect |
| 4. #20292890 | C2 | direct (N × H) |
| 5. C2×#16812045 | C2 | semidirect |
| 6. C2×#16812027 | C2 | semidirect |
| 7. C2×#16812025 | C2 | semidirect |
| 8. C2×#131×C107 | C2 | semidirect |
| 12. #16812139 | C22 | semidirect |
| 19. C2×#13133807 | C22 | semidirect |
| 25. #16812045 | C22 | semidirect |
| 26. #16812027 | C22 | semidirect |
| 27. #16812025 | C22 | semidirect |
| 30. #131×C107 | C22 | semidirect |
| 135. C2×C107 | #471 | semidirect |
| 139. C107 | C2×#471 | semidirect |
| 143. C2×#131 | D107 | semidirect |
| 164. #131 | C2×D107 | semidirect |
| 275. C2 | #20292890 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812139 | 2 |
| C2×#16812134 | 2 |
| C22×#13133807 | 2 |
| #20292890 | 2 |
| C2×#16812045 | 2 |
| C2×#16812027 | 2 |
| C2×#16812025 | 2 |
| C2×#131×C107 | 2 |
| C2×#471 | 107 |