Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #11719530 | C2 | semidirect |
| 3. C13×#408 | C2 | semidirect |
| 4. #11718795 | C2 | semidirect |
| 5. #11718775 | C2 | semidirect |
| 6. #11718399 | C2 | semidirect |
| 7. #11718398 | C2 | semidirect |
| 8. #11718392 | C2 | semidirect |
| 9. #11718384 | C2 | semidirect |
| 12. C22×Dic26 | C22 | semidirect |
| 13. C2×C13×M16 | C22 | semidirect |
| 14. C22×C8×C13 | C22 | semidirect |
| 26. #88180 | C22 | semidirect |
| 28. #88178 | C22 | semidirect |
| 32. C13×C22⋊C8 | C22 | semidirect |
| 35. #88058 | C22 | semidirect |
| 36. #88057 | C22 | semidirect |
| 37. #88056 | C22 | semidirect |
| 38. #88056 | C22 | semidirect |
| 121. #408 | D13 | semidirect |
| 146. C2×M16 | C2×D13 | semidirect |
| 147. C22×C8 | C2×D13 | semidirect |
| 169. C22⋊C8 | C2×D13 | semidirect |
| 215. C13 | #3200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719535 | 2 |
| #11719530 | 2 |
| C13×#408 | 2 |
| #11718795 | 2 |
| #11718775 | 2 |
| #11718399 | 2 |
| #11718398 | 2 |
| #11718392 | 2 |
| #11718384 | 2 |
| #3200 | 13 |