Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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. #11719290 | C2 | semidirect |
| 2. #11719282 | C2 | semidirect |
| 3. C13×#446 | C2 | semidirect |
| 4. #11718509 | C2 | semidirect |
| 5. #11718505 | C2 | semidirect |
| 6. #11718504 | C2 | semidirect |
| 7. #11718504 | C2 | semidirect |
| 8. #11718373 | C2 | semidirect |
| 9. #11718372 | C2 | semidirect |
| 10. #11718356 | C2 | semidirect |
| 11. C4×#6095 | C2 | semidirect |
| 109. C8×C13 | #41 | semidirect |
| 118. #446 | D13 | semidirect |
| 211. C13 | #3399 | semidirect |
| 243. C8 | #6131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719290 | 2 |
| #11719282 | 2 |
| C13×#446 | 2 |
| #11718509 | 2 |
| #11718505 | 2 |
| #11718504 | 2 |
| #11718373 | 2 |
| #11718372 | 2 |
| #11718356 | 2 |
| C4×#6095 | 2 |
| #3399 | 13 |