Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #11719184 | C2 | semidirect |
| 2. #11719182 | C2 | semidirect |
| 3. C13×#432 | C2 | semidirect |
| 4. #11718506 | C2 | semidirect |
| 5. #11718505 | C2 | semidirect |
| 6. #11718395 | C2 | semidirect |
| 7. #11718394 | C2 | semidirect |
| 8. #11718376 | C2 | semidirect |
| 9. #11718374 | C2 | semidirect |
| 10. #11718373 | C2 | semidirect |
| 11. #11718364 | C2 | semidirect |
| 125. #432 | D13 | semidirect |
| 224. C13 | #3219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719184 | 2 |
| #11719182 | 2 |
| C13×#432 | 2 |
| #11718506 | 2 |
| #11718505 | 2 |
| #11718395 | 2 |
| #11718394 | 2 |
| #11718376 | 2 |
| #11718374 | 2 |
| #11718373 | 2 |
| #11718364 | 2 |
| #3219 | 13 |