Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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×#16812115 | C2 | semidirect |
| 2. #20293194 | C2 | semidirect |
| 3. #20292877 | C2 | semidirect |
| 4. #20292860 | C2 | semidirect |
| 5. #20292665 | C2 | semidirect |
| 6. #20292632 | C2 | semidirect |
| 7. C22×D8×C107 | C2 | semidirect |
| 11. C2×#13133801 | C22 | semidirect |
| 12. C2×C8×D107 | C22 | semidirect |
| 15. #16812080 | C22 | semidirect |
| 18. #16812043 | C22 | semidirect |
| 19. #16812041 | C22 | semidirect |
| 20. #16812030 | C22 | semidirect |
| 49. C2×C8×C107 | D4 | semidirect |
| 94. C107 | #3058 | semidirect |
| 95. C22×D8 | D107 | semidirect |
| 139. 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×#16812115 | 2 |
| #20293194 | 2 |
| #20292877 | 2 |
| #20292860 | 2 |
| #20292665 | 2 |
| #20292632 | 2 |
| C22×D8×C107 | 2 |
| #3058 | 107 |