Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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×C13×#135 | C2 | semidirect |
| 2. #11719535 | C2 | semidirect |
| 3. C2×#88203 | C2 | semidirect |
| 4. C22×D104 | C2 | semidirect |
| 5. #11718852 | C2 | semidirect |
| 6. #11718837 | C2 | semidirect |
| 7. #11718812 | C2 | semidirect |
| 8. #11718762 | C2 | semidirect |
| 12. C2×C13×Q16 | C22 | semidirect |
| 13. C2×C13×SD16 | C22 | semidirect |
| 14. C2×C13×D8 | C22 | semidirect |
| 17. #88201 | C22 | semidirect |
| 18. C2×#6106 | C22 | semidirect |
| 19. #88194 | C22 | semidirect |
| 21. C2×#6104 | C22 | semidirect |
| 28. #88055 | C22 | semidirect |
| 29. C8×Dic13 | C22 | semidirect |
| 46. C2×C8×C13 | D4 | semidirect |
| 55. #6099 | D4 | semidirect |
| 85. C2×#135 | D13 | semidirect |
| 109. C2×Q16 | C2×D13 | semidirect |
| 111. C2×SD16 | C2×D13 | semidirect |
| 116. C2×D8 | C2×D13 | semidirect |
| 153. C2×C8 | C22⋊D13 | semidirect |
| 160. C13 | #3155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#135 | 2 |
| #11719535 | 2 |
| C2×#88203 | 2 |
| C22×D104 | 2 |
| #11718852 | 2 |
| #11718837 | 2 |
| #11718812 | 2 |
| #11718762 | 2 |
| #3155 | 13 |