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. C13×#575 | C2 | semidirect |
| 2. C2×#88203 | C2 | semidirect |
| 3. C2×#88203 | C2 | semidirect |
| 4. #11719524 | C2 | semidirect |
| 5. #11718898 | C2 | semidirect |
| 6. #11718864 | C2 | semidirect |
| 7. #11718860 | C2 | semidirect |
| 8. C2×#88063 | C2 | semidirect |
| 9. #11718785 | C2 | semidirect |
| 14. C13×#137 | C22 | semidirect |
| 16. C13×AGL(1,ℤ/8) | C22 | semidirect |
| 24. #88202 | C22 | semidirect |
| 26. C2×#6106 | C22 | semidirect |
| 28. C2×#6104 | C22 | semidirect |
| 33. #88076 | C22 | semidirect |
| 34. #88073 | C22 | semidirect |
| 35. #88063 | C22 | semidirect |
| 36. #88062 | C22 | semidirect |
| 123. #575 | D13 | semidirect |
| 154. #137 | C2×D13 | semidirect |
| 160. AGL(1,ℤ/8) | C2×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 |
|---|---|
| C13×#575 | 2 |
| C2×#88203 | 2 |
| #11719524 | 2 |
| #11718898 | 2 |
| #11718864 | 2 |
| #11718860 | 2 |
| C2×#88063 | 2 |
| #11718785 | 2 |
| #3068 | 13 |