Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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×#16812131 | C2 | semidirect |
| 2. #20293138 | C2 | semidirect |
| 3. #20292885 | C2 | semidirect |
| 4. #20292880 | C2 | semidirect |
| 5. #20292873 | C2 | semidirect |
| 6. #20292665 | C2 | semidirect |
| 7. #20292624 | C2 | semidirect |
| 8. C22×M16×C107 | C2 | semidirect |
| 11. C2×Dic428 | C22 | semidirect |
| 12. C2×#13133807 | C22 | semidirect |
| 13. C2×D856 | C22 | semidirect |
| 20. #16812043 | C22 | semidirect |
| 21. #16812041 | C22 | semidirect |
| 22. #16812034 | C22 | semidirect |
| 23. #16812031 | C22 | semidirect |
| 56. C2×C8×C107 | D4 | semidirect |
| 106. C107 | #3054 | semidirect |
| 108. C22×M16 | D107 | semidirect |
| 156. C2×C8 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| #20293138 | 2 |
| #20292885 | 2 |
| #20292880 | 2 |
| #20292873 | 2 |
| #20292665 | 2 |
| #20292624 | 2 |
| C22×M16×C107 | 2 |
| #3054 | 107 |