Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 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×#131 | C2 | semidirect |
| 2. #11719538 | C2 | semidirect |
| 3. #11719535 | C2 | semidirect |
| 4. C2×#88162 | C2 | semidirect |
| 5. #11718796 | C2 | semidirect |
| 6. #11718795 | C2 | semidirect |
| 7. #11718782 | C2 | semidirect |
| 8. #11718776 | C2 | semidirect |
| 9. #11718775 | C2 | semidirect |
| 10. #11718774 | C2 | semidirect |
| 11. C2×#88061 | C2 | semidirect |
| 17. C2×C13×M16 | C22 | semidirect |
| 19. C22×C8×C13 | C22 | semidirect |
| 28. #88184 | C22 | semidirect |
| 31. #88178 | C22 | semidirect |
| 37. #88061 | C22 | semidirect |
| 38. #88061 | C22 | semidirect |
| 39. #88058 | C22 | semidirect |
| 40. #88057 | C22 | semidirect |
| 41. #88056 | C22 | semidirect |
| 42. #88056 | C22 | semidirect |
| 66. C13×M16 | D4 | semidirect |
| 124. C2×#131 | D13 | semidirect |
| 164. C2×M16 | C2×D13 | semidirect |
| 166. C22×C8 | C2×D13 | semidirect |
| 219. M16 | C22⋊D13 | semidirect |
| 236. C13 | #3062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#131 | 2 |
| #11719538 | 2 |
| #11719535 | 2 |
| C2×#88162 | 2 |
| #11718796 | 2 |
| #11718795 | 2 |
| #11718782 | 2 |
| #11718776 | 2 |
| #11718775 | 2 |
| #11718774 | 2 |
| C2×#88061 | 2 |
| #3062 | 13 |