Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. #11719275 | C2 | semidirect |
| 5. #11718681 | C2 | semidirect |
| 7. #11718517 | C2 | semidirect |
| 8. #11718455 | C2 | semidirect |
| 10. #11718343 | C2 | semidirect |
| 11. #11718340 | C2 | semidirect |
| 50. C13×SD16 | Q8 | semidirect |
| 76. Q8×C13 | C2×Q8 | semidirect |
| 96. C8×C13 | C2×Q8 | semidirect |
| 166. SD16 | Dic26 | semidirect |
| 189. C13 | #3386 | semidirect |
| 196. Q8 | C2×Dic26 | semidirect |
| 213. C8 | C2×Dic26 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719275 | 2 |
| D4×Dic26 | 2 |
| C4×C13×SD16 | 2 |
| #11718825 | 2 |
| #11718681 | 2 |
| #11718668 | 2 |
| #11718517 | 2 |
| #11718455 | 2 |
| #11718427 | 2 |
| #11718343 | 2 |
| #11718340 | 2 |
| #3386 | 13 |