Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
792 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 229 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×C8×D107 | C2 | semidirect |
| 3. C2×#16812067 | C2 | semidirect |
| 4. #20292620 | C2 | direct (N × H) |
| 5. C2×#16812034 | C2 | semidirect |
| 6. C2×#16812032 | C2 | semidirect |
| 7. C2×#16812030 | C2 | semidirect |
| 8. C2×#102×C107 | C2 | semidirect |
| 11. C2×#13133817 | C4 | semidirect |
| 19. C2×C8×D107 | C22 | semidirect |
| 21. #16812067 | C22 | semidirect |
| 25. #16812034 | C22 | semidirect |
| 26. #16812032 | C22 | semidirect |
| 27. #16812030 | C22 | semidirect |
| 31. #102×C107 | C22 | semidirect |
| 35. #13133817 | C2×C4 | semidirect |
| 123. C2×C107 | #416 | semidirect |
| 129. C107 | C2×#416 | semidirect |
| 137. C2×#102 | D107 | semidirect |
| 160. #102 | C2×D107 | semidirect |
| 253. C2 | #20292620 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133817 | 2 |
| C22×C8×D107 | 2 |
| C2×#16812067 | 2 |
| #20292620 | 2 |
| C2×#16812034 | 2 |
| C2×#16812032 | 2 |
| C2×#16812030 | 2 |
| C2×#102×C107 | 2 |
| C2×#416 | 107 |