Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 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 |
|---|---|---|
| 1. C2×#16812156 | C2 | semidirect |
| 2. C2×#16812135 | C2 | semidirect |
| 3. C2×#16812096 | C2 | semidirect |
| 4. #20292798 | C2 | direct (N × H) |
| 5. C2×#16812036 | C2 | semidirect |
| 6. C2×#16812035 | C2 | semidirect |
| 7. C2×#16812027 | C2 | semidirect |
| 8. C2×AGL(1,ℤ/8)×C107 | C2 | semidirect |
| 12. #16812156 | C22 | semidirect |
| 21. #16812135 | C22 | semidirect |
| 26. #16812096 | C22 | semidirect |
| 29. #16812036 | C22 | semidirect |
| 30. #16812035 | C22 | semidirect |
| 31. #16812027 | C22 | semidirect |
| 35. AGL(1,ℤ/8)×C107 | C22 | semidirect |
| 172. C2×C107 | #454 | semidirect |
| 176. C107 | C2×#454 | semidirect |
| 179. C2×AGL(1,ℤ/8) | D107 | semidirect |
| 201. AGL(1,ℤ/8) | C2×D107 | semidirect |
| 349. C2 | #20292798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812156 | 2 |
| C2×#16812135 | 2 |
| C2×#16812096 | 2 |
| #20292798 | 2 |
| C2×#16812036 | 2 |
| C2×#16812035 | 2 |
| C2×#16812027 | 2 |
| C2×AGL(1,ℤ/8)×C107 | 2 |
| C2×#454 | 107 |