Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#16812137 | C2 | semidirect |
| 2. #20293177 | C2 | semidirect |
| 3. C2×C4×D428 | C2 | semidirect |
| 4. #20292843 | C2 | semidirect |
| 5. #20292833 | C2 | semidirect |
| 6. #20292823 | C2 | semidirect |
| 7. #20292629 | C2 | semidirect |
| 8. #423×C107 | C2 | semidirect |
| 15. #16812109 | C22 | semidirect |
| 16. #16812106 | C22 | semidirect |
| 17. #16812097 | C22 | semidirect |
| 28. #16812034 | C22 | semidirect |
| 29. #16812031 | C22 | semidirect |
| 32. C4⋊C8×C107 | C22 | semidirect |
| 33. C4⋊C8×C107 | C22 | semidirect |
| 42. C2×D428 | D4 | semidirect |
| 118. C4×C107 | AGL(1,ℤ/8) | semidirect |
| 130. C107 | #3036 | semidirect |
| 137. #423 | D107 | semidirect |
| 160. C4⋊C8 | C2×D107 | semidirect |
| 161. C4⋊C8 | C2×D107 | semidirect |
| 250. C4 | #16812137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812137 | 2 |
| #20293177 | 2 |
| C2×C4×D428 | 2 |
| #20292843 | 2 |
| #20292833 | 2 |
| #20292823 | 2 |
| #20292629 | 2 |
| #423×C107 | 2 |
| #3036 | 107 |