Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
| 3. C4×C13×SD16 | C2 | semidirect |
| 4. #11718824 | C2 | semidirect |
| 5. #11718688 | C2 | semidirect |
| 6. #11718669 | C2 | semidirect |
| 7. #11718531 | C2 | semidirect |
| 8. #11718449 | C2 | semidirect |
| 9. #11718421 | C2 | semidirect |
| 10. #11718355 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 78. Q8×C13 | #41 | semidirect |
| 100. Dic26 | SD16 | semidirect |
| 114. C4×SD16 | D13 | semidirect |
| 199. C13 | #3362 | semidirect |
| 206. Q8 | #6127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic26 | 2 |
| #11719258 | 2 |
| C4×C13×SD16 | 2 |
| #11718824 | 2 |
| #11718688 | 2 |
| #11718669 | 2 |
| #11718531 | 2 |
| #11718449 | 2 |
| #11718421 | 2 |
| #11718355 | 2 |
| C8×Dic26 | 2 |
| #3362 | 13 |