Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #11719527 | C2 | semidirect |
| 3. #11719524 | C2 | semidirect |
| 4. C2×#88186 | C2 | semidirect |
| 5. C2×#88073 | C2 | semidirect |
| 6. #11718861 | C2 | semidirect |
| 7. #11718860 | C2 | semidirect |
| 8. #11718793 | C2 | semidirect |
| 9. #11718785 | C2 | semidirect |
| 18. #88205 | C22 | semidirect |
| 20. #88203 | C22 | semidirect |
| 22. #88202 | C22 | semidirect |
| 24. C2×#6105 | C22 | semidirect |
| 28. C2×#6104 | C22 | semidirect |
| 33. #88073 | C22 | semidirect |
| 34. #88064 | C22 | semidirect |
| 35. #88063 | C22 | semidirect |
| 36. #88062 | C22 | semidirect |
| 125. C2×AGL(1,ℤ/8) | D13 | semidirect |
| 230. C13 | #3068 | 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 |
| #11719527 | 2 |
| #11719524 | 2 |
| C2×#88186 | 2 |
| C2×#88073 | 2 |
| #11718861 | 2 |
| #11718860 | 2 |
| #11718793 | 2 |
| #11718785 | 2 |
| #3068 | 13 |