Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #11719223 | C2 | semidirect |
| 3. #11718900 | C2 | semidirect |
| 4. #11718879 | C2 | semidirect |
| 5. #11718737 | C2 | semidirect |
| 6. #11718736 | C2 | semidirect |
| 7. #11718732 | C2 | semidirect |
| 8. #11718721 | C2 | semidirect |
| 9. #11718717 | C2 | semidirect |
| 10. #11718715 | C2 | semidirect |
| 11. #11718661 | C2 | semidirect |
| 21. C2×#6107 | C22 | semidirect |
| 24. C2×#6105 | C22 | semidirect |
| 28. #88124 | C22 | semidirect |
| 29. #88123 | C22 | semidirect |
| 30. C4×Dic26 | C22 | semidirect |
| 31. #88075 | C22 | semidirect |
| 34. #88072 | C22 | semidirect |
| 36. C4⋊#1055 | C22 | semidirect |
| 37. #88043 | C22 | semidirect |
| 38. C4×#1055 | C22 | semidirect |
| 194. C13 | #3222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#535 | 2 |
| #11719223 | 2 |
| #11718900 | 2 |
| #11718879 | 2 |
| #11718737 | 2 |
| #11718736 | 2 |
| #11718732 | 2 |
| #11718721 | 2 |
| #11718717 | 2 |
| #11718715 | 2 |
| #11718661 | 2 |
| #3222 | 13 |