Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #11719221 | C2 | semidirect |
| 5. #11718679 | C2 | semidirect |
| 6. C4×#6105 | C2 | semidirect |
| 7. #11718665 | C2 | semidirect |
| 8. #11718659 | C2 | semidirect |
| 9. #11718658 | C2 | semidirect |
| 17. C2×#6105 | C4 | semidirect |
| 25. C4×Dic26 | C22 | semidirect |
| 27. #88050 | C22 | semidirect |
| 28. #88048 | C22 | semidirect |
| 29. #88047 | C22 | semidirect |
| 30. #88043 | C22 | semidirect |
| 31. C4×#1055 | C22 | semidirect |
| 42. C2×Dic26 | C2×C4 | semidirect |
| 52. #6105 | C2×C4 | semidirect |
| 53. #6105 | C2×C4 | semidirect |
| 59. C2×#1055 | C2×C4 | semidirect |
| 166. C13 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#518 | 2 |
| C22×#6105 | 2 |
| #11719221 | 2 |
| #11718876 | 2 |
| #11718679 | 2 |
| C4×#6105 | 2 |
| #11718665 | 2 |
| #11718659 | 2 |
| #11718658 | 2 |
| #2949 | 13 |