Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 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×#16812142 | C2 | semidirect |
| 3. C22×#13133807 | C2 | semidirect |
| 4. C2×#16812115 | C2 | semidirect |
| 5. #20292891 | C2 | direct (N × H) |
| 6. C2×#16812027 | C2 | semidirect |
| 7. C2×#16812025 | C2 | semidirect |
| 8. C2×#108×C107 | C2 | semidirect |
| 13. #16812142 | C22 | semidirect |
| 22. C2×#13133807 | C22 | semidirect |
| 25. #16812115 | C22 | semidirect |
| 29. #16812027 | C22 | semidirect |
| 30. #16812025 | C22 | semidirect |
| 34. #108×C107 | C22 | semidirect |
| 134. C2×C107 | #471 | semidirect |
| 139. C107 | C2×#471 | semidirect |
| 145. C2×#108 | D107 | semidirect |
| 171. #108 | C2×D107 | semidirect |
| 275. C2 | #20292891 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812142 | 2 |
| C2×#16812137 | 2 |
| C22×#13133807 | 2 |
| C2×#16812115 | 2 |
| #20292891 | 2 |
| C2×#16812027 | 2 |
| C2×#16812025 | 2 |
| C2×#108×C107 | 2 |
| C2×#471 | 107 |