Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
| 4. #11718680 | C2 | semidirect |
| 5. #11718679 | C2 | semidirect |
| 6. C4×#6105 | C2 | semidirect |
| 7. #11718670 | C2 | semidirect |
| 8. #11718661 | C2 | semidirect |
| 9. #11718657 | C2 | semidirect |
| 22. #88124 | C22 | semidirect |
| 23. #88123 | C22 | semidirect |
| 24. C4×Dic26 | C22 | semidirect |
| 28. #88050 | C22 | semidirect |
| 29. #88050 | C22 | semidirect |
| 30. #88048 | C22 | semidirect |
| 31. #88047 | C22 | semidirect |
| 32. C4⋊#1055 | C22 | semidirect |
| 33. #88043 | C22 | semidirect |
| 34. C4×#1055 | C22 | semidirect |
| 165. C13 | #3123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#518 | 2 |
| #11719223 | 2 |
| #11718879 | 2 |
| #11718680 | 2 |
| #11718679 | 2 |
| C4×#6105 | 2 |
| #11718670 | 2 |
| #11718661 | 2 |
| #11718657 | 2 |
| #3123 | 13 |