Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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. Q8⋊#1055 | C2 | semidirect |
| 6. #11718078 | C2 | semidirect |
| 7. #11718076 | C2 | semidirect |
| 52. Q8×C13 | SD16 | semidirect |
| 139. C13 | #1626 | semidirect |
| 146. Q8 | #6105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719275 | 2 |
| C13×#460 | 2 |
| #11718736 | 2 |
| #11718731 | 2 |
| Q8⋊#1055 | 2 |
| #11718078 | 2 |
| #11718076 | 2 |
| #1626 | 13 |