Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 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. C2×#16812131 | C2 | semidirect |
| 2. #20293070 | C2 | semidirect |
| 3. #20293065 | C2 | semidirect |
| 4. #20293059 | C2 | semidirect |
| 5. C2×M32×C107 | C2 | semidirect |
| 10. #16812131 | C22 | semidirect |
| 11. C2×Dic428 | C22 | semidirect |
| 13. C2×D856 | C22 | semidirect |
| 14. Dic856 | C22 | semidirect |
| 15. #16812054 | C22 | semidirect |
| 16. D1712 | C22 | semidirect |
| 18. M32×C107 | C22 | semidirect |
| 19. C2×C16×C107 | C22 | semidirect |
| 72. C107 | #3414 | semidirect |
| 77. C2×M32 | D107 | semidirect |
| 90. M32 | C2×D107 | semidirect |
| 91. C2×C16 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| #20293070 | 2 |
| #20293065 | 2 |
| #20293059 | 2 |
| C2×M32×C107 | 2 |
| #3414 | 107 |