Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 340 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. Q8×Dic26 | C2 | semidirect |
| 5. #11718682 | C2 | semidirect |
| 7. #11718517 | C2 | semidirect |
| 8. #11718457 | C2 | semidirect |
| 10. #11718343 | C2 | semidirect |
| 11. #11718340 | C2 | semidirect |
| 49. C13×SD16 | Q8 | semidirect |
| 164. SD16 | Dic26 | semidirect |
| 187. C13 | #3385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic26 | 2 |
| #11719248 | 2 |
| C4×C13×SD16 | 2 |
| #11718825 | 2 |
| #11718682 | 2 |
| #11718669 | 2 |
| #11718517 | 2 |
| #11718457 | 2 |
| #11718420 | 2 |
| #11718343 | 2 |
| #11718340 | 2 |
| #3385 | 13 |