Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
410 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×C13×#97 | C2 | semidirect |
| 4. #11718776 | C2 | semidirect |
| 5. #11718775 | C2 | semidirect |
| 6. #11718375 | C2 | semidirect |
| 7. #11718374 | C2 | semidirect |
| 8. #11718373 | C2 | semidirect |
| 9. #11718372 | C2 | semidirect |
| 10. #11718371 | C2 | semidirect |
| 11. #11718363 | C2 | semidirect |
| 111. C8×C13 | #41 | semidirect |
| 122. C2×#97 | D13 | semidirect |
| 219. C13 | #3180 | semidirect |
| 248. C8 | #6127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719184 | 2 |
| #11719182 | 2 |
| C2×C13×#97 | 2 |
| #11718776 | 2 |
| #11718775 | 2 |
| #11718375 | 2 |
| #11718374 | 2 |
| #11718373 | 2 |
| #11718372 | 2 |
| #11718371 | 2 |
| #11718363 | 2 |
| #3180 | 13 |