Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719289 | C2 | semidirect |
| 3. C4×C13×SD16 | C2 | semidirect |
| 4. #11718835 | C2 | semidirect |
| 5. #11718681 | C2 | semidirect |
| 6. #11718668 | C2 | semidirect |
| 7. #11718522 | C2 | semidirect |
| 8. #11718470 | C2 | semidirect |
| 9. #11718445 | C2 | semidirect |
| 10. #11718349 | C2 | semidirect |
| 11. #11718343 | C2 | semidirect |
| 99. C8×C13 | #41 | semidirect |
| 109. C4×SD16 | D13 | semidirect |
| 196. C13 | #3353 | semidirect |
| 222. C8 | #6127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719289 | 2 |
| #11719256 | 2 |
| C4×C13×SD16 | 2 |
| #11718835 | 2 |
| #11718681 | 2 |
| #11718668 | 2 |
| #11718522 | 2 |
| #11718470 | 2 |
| #11718445 | 2 |
| #11718349 | 2 |
| #11718343 | 2 |
| #3353 | 13 |