Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×C13×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #11719535 | C2 | semidirect |
| 3. #11719503 | C2 | semidirect |
| 4. C22×#6104 | C2 | semidirect |
| 5. #11718894 | C2 | semidirect |
| 6. #11718826 | C2 | semidirect |
| 7. #11718811 | C2 | semidirect |
| 8. #11718792 | C2 | semidirect |
| 9. #11718780 | C2 | semidirect |
| 14. C2×C13×SD16 | C22 | semidirect |
| 15. C2×C13×D8 | C22 | semidirect |
| 18. #88201 | C22 | semidirect |
| 19. #88194 | C22 | semidirect |
| 22. D4×Dic13 | C22 | semidirect |
| 29. #88075 | C22 | semidirect |
| 30. #88072 | C22 | semidirect |
| 31. #88061 | C22 | semidirect |
| 32. #88054 | C22 | semidirect |
| 41. C2×D4×C13 | D4 | semidirect |
| 99. C2×AGL(1,ℤ/8) | D13 | semidirect |
| 129. C2×SD16 | C2×D13 | semidirect |
| 132. C2×D8 | C2×D13 | semidirect |
| 167. C2×D4 | C22⋊D13 | semidirect |
| 188. C13 | #3041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×AGL(1,ℤ/8) | 2 |
| #11719535 | 2 |
| #11719503 | 2 |
| C22×#6104 | 2 |
| #11718894 | 2 |
| #11718826 | 2 |
| #11718811 | 2 |
| #11718792 | 2 |
| #11718780 | 2 |
| #3041 | 13 |