Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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×#88162 | C2 | semidirect |
| 2. C2×#88158 | C2 | semidirect |
| 3. #11719230 | C2 | semidirect |
| 4. #11719228 | C2 | semidirect |
| 5. C13×#424 | C2 | semidirect |
| 6. #11718794 | C2 | semidirect |
| 7. C2×#88061 | C2 | semidirect |
| 8. #11718509 | C2 | semidirect |
| 9. #11718506 | C2 | semidirect |
| 10. #11718505 | C2 | semidirect |
| 11. #11718504 | C2 | semidirect |
| 20. C2×Dic52 | C22 | semidirect |
| 23. C2×D104 | C22 | semidirect |
| 25. C2×#6095 | C22 | semidirect |
| 26. C2×#6095 | C22 | semidirect |
| 35. C4×D52 | C22 | semidirect |
| 36. C4×Dic26 | C22 | semidirect |
| 37. C13×C4⋊C8 | C22 | semidirect |
| 38. C13×C4⋊C8 | C22 | semidirect |
| 41. #88061 | C22 | semidirect |
| 42. #88056 | C22 | semidirect |
| 51. #6127 | D4 | semidirect |
| 134. #424 | D13 | semidirect |
| 184. C4⋊C8 | C2×D13 | semidirect |
| 185. C4⋊C8 | C2×D13 | semidirect |
| 241. C13 | #3045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88162 | 2 |
| C2×#88158 | 2 |
| #11719230 | 2 |
| #11719228 | 2 |
| C13×#424 | 2 |
| #11718794 | 2 |
| C2×#88061 | 2 |
| #11718509 | 2 |
| #11718506 | 2 |
| #11718505 | 2 |
| #11718504 | 2 |
| #3045 | 13 |