Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 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. #11719284 | C2 | semidirect |
| 2. #11719282 | C2 | semidirect |
| 3. C13×#446 | C2 | semidirect |
| 4. #11718508 | C2 | semidirect |
| 5. #11718504 | C2 | semidirect |
| 6. #11718504 | C2 | semidirect |
| 7. #11718503 | C2 | semidirect |
| 8. #11718374 | C2 | semidirect |
| 9. #11718372 | C2 | semidirect |
| 10. #11718355 | C2 | semidirect |
| 11. C4×D104 | C2 | semidirect |
| 96. D52 | #41 | semidirect |
| 113. #446 | D13 | semidirect |
| 203. C13 | #3366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719284 | 2 |
| #11719282 | 2 |
| C13×#446 | 2 |
| #11718508 | 2 |
| #11718504 | 2 |
| #11718503 | 2 |
| #11718374 | 2 |
| #11718372 | 2 |
| #11718355 | 2 |
| C4×D104 | 2 |
| #3366 | 13 |