Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 2. C2×#16812068 | C2 | semidirect |
| 3. #20292952 | C2 | direct (N × H) |
| 4. C2×#16812043 | C2 | semidirect |
| 5. C2×#16812041 | C2 | semidirect |
| 6. C2×#16812031 | C2 | semidirect |
| 7. C2×#16812031 | C2 | semidirect |
| 8. C2×C22⋊C8×C107 | C2 | semidirect |
| 14. #16812068 | C22 | semidirect |
| 21. #16812043 | C22 | semidirect |
| 22. #16812041 | C22 | semidirect |
| 23. #16812031 | C22 | semidirect |
| 24. #16812031 | C22 | semidirect |
| 28. C22⋊C8×C107 | C22 | semidirect |
| 109. C2×C107 | #482 | semidirect |
| 115. C107 | C2×#482 | semidirect |
| 123. C2×C22⋊C8 | D107 | semidirect |
| 143. C22⋊C8 | C2×D107 | semidirect |
| 225. C2 | #20292952 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812083 | 2 |
| C2×#16812068 | 2 |
| #20292952 | 2 |
| C2×#16812043 | 2 |
| C2×#16812041 | 2 |
| C2×#16812031 | 2 |
| C2×C22⋊C8×C107 | 2 |
| C2×#482 | 107 |