Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#88178 | C2 | semidirect |
| 4. #11718873 | C2 | semidirect |
| 5. #11718871 | C2 | semidirect |
| 6. #11718610 | C2 | semidirect |
| 7. #11718609 | C2 | semidirect |
| 8. #11718608 | C2 | semidirect |
| 12. C22×Dic26 | C22 | semidirect |
| 20. C2×C4⋊Dic13 | C22 | semidirect |
| 21. C2×C4⋊Dic13 | C22 | semidirect |
| 23. C2×#6101 | C22 | semidirect |
| 24. C2×#6101 | C22 | semidirect |
| 25. #88071 | C22 | semidirect |
| 26. #88071 | C22 | semidirect |
| 31. C24×C13 | Q8 | semidirect |
| 148. C24 | Dic26 | semidirect |
| 173. C13 | #2626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×C22⋊C4 | 2 |
| C2×#88178 | 2 |
| #11718908 | 2 |
| #11718873 | 2 |
| #11718871 | 2 |
| #11718610 | 2 |
| #11718609 | 2 |
| #11718608 | 2 |
| #2626 | 13 |