Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C2×#16812071 | C2 | semidirect |
| 3. #20292738 | C2 | direct (N × H) |
| 4. C2×#16812029 | C2 | semidirect |
| 5. C2×#16812019 | C2 | semidirect |
| 6. C2×#106×C107 | C2 | semidirect |
| 9. C2×D856 | C4 | semidirect |
| 13. #16812071 | C22 | semidirect |
| 16. #16812029 | C22 | semidirect |
| 17. #16812019 | C22 | semidirect |
| 20. #106×C107 | C22 | semidirect |
| 24. C2×D428 | C2×C4 | semidirect |
| 29. D856 | C2×C4 | semidirect |
| 37. C2×C8×C107 | C2×C4 | semidirect |
| 56. D428 | C22×C4 | semidirect |
| 58. C8×C107 | C22×C4 | semidirect |
| 72. C2×C107 | #442 | semidirect |
| 77. C107 | C2×#442 | semidirect |
| 81. C2×#106 | D107 | semidirect |
| 95. #106 | C2×D107 | semidirect |
| 111. C2×C8 | C4×D107 | semidirect |
| 136. C8 | C2×C4×D107 | semidirect |
| 150. C2 | #20292738 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D856 | 2 |
| C2×#16812071 | 2 |
| #20292738 | 2 |
| C2×#16812029 | 2 |
| C2×#16812019 | 2 |
| C2×#106×C107 | 2 |
| C2×#442 | 107 |