Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20293432 | C2 | semidirect |
| 2. #20293065 | C2 | semidirect |
| 3. #20293059 | C2 | semidirect |
| 4. C2×D1712 | C2 | semidirect |
| 5. #504×C107 | C2 | semidirect |
| 8. #16812131 | C22 | semidirect |
| 9. C2×D856 | C22 | semidirect |
| 10. Dic856 | C22 | semidirect |
| 11. #16812054 | C22 | semidirect |
| 12. D1712 | C22 | semidirect |
| 13. D1712 | C22 | semidirect |
| 15. M32×C107 | C22 | semidirect |
| 16. C2×C16×C107 | C22 | semidirect |
| 51. C107 | #3415 | semidirect |
| 56. #504 | D107 | semidirect |
| 66. M32 | C2×D107 | semidirect |
| 67. C2×C16 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293432 | 2 |
| #20293065 | 2 |
| #20293059 | 2 |
| C2×D1712 | 2 |
| #504×C107 | 2 |
| #3415 | 107 |