Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11719260 | C2 | semidirect |
| 2. #11719256 | C2 | semidirect |
| 3. C13×#436 | C2 | semidirect |
| 4. #11718795 | C2 | semidirect |
| 5. #11718794 | C2 | semidirect |
| 6. #11718507 | C2 | semidirect |
| 7. #11718502 | C2 | semidirect |
| 8. #11718395 | C2 | semidirect |
| 9. #11718383 | C2 | semidirect |
| 10. C4×D104 | C2 | semidirect |
| 11. #11718342 | C2 | semidirect |
| 98. D52 | #41 | semidirect |
| 117. #436 | D13 | semidirect |
| 209. C13 | #3330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719260 | 2 |
| #11719256 | 2 |
| C13×#436 | 2 |
| #11718795 | 2 |
| #11718794 | 2 |
| #11718507 | 2 |
| #11718502 | 2 |
| #11718395 | 2 |
| #11718383 | 2 |
| C4×D104 | 2 |
| #11718342 | 2 |
| #3330 | 13 |