Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#13133805 | C2 | semidirect |
| 3. C2×#16812085 | C2 | semidirect |
| 4. #20292788 | C2 | direct (N × H) |
| 5. C2×#16812033 | C2 | semidirect |
| 6. C2×#16812031 | C2 | semidirect |
| 7. C2×(C2×D107)⋊C8 | C2 | semidirect |
| 8. C22×Q16×C107 | C2 | semidirect |
| 18. C2×#13133805 | C22 | semidirect |
| 21. #16812085 | C22 | semidirect |
| 25. #16812033 | C22 | semidirect |
| 26. #16812031 | C22 | semidirect |
| 27. (C2×D107)⋊C8 | C22 | semidirect |
| 31. C2×Q16×C107 | C22 | semidirect |
| 129. C2×C107 | #452 | semidirect |
| 136. C107 | C2×#452 | semidirect |
| 138. C22×Q16 | D107 | semidirect |
| 156. C2×Q16 | C2×D107 | semidirect |
| 267. C2 | #20292788 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133819 | 2 |
| C22×#13133805 | 2 |
| C2×#16812085 | 2 |
| #20292788 | 2 |
| C2×#16812033 | 2 |
| C2×#16812031 | 2 |
| C2×(C2×D107)⋊C8 | 2 |
| C22×Q16×C107 | 2 |
| C2×#452 | 107 |