Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
426 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 426 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. #11719432 | C2 | semidirect |
| 2. #11719258 | C2 | semidirect |
| 3. C13×#474 | C2 | semidirect |
| 4. #11718749 | C2 | semidirect |
| 5. C4×#6104 | C2 | semidirect |
| 6. #11718551 | C2 | semidirect |
| 7. #11718533 | C2 | semidirect |
| 8. #11718504 | C2 | semidirect |
| 9. #11718491 | C2 | semidirect |
| 10. #11718447 | C2 | semidirect |
| 11. #11718421 | C2 | semidirect |
| 98. D52 | #41 | semidirect |
| 103. Dic26 | D8 | semidirect |
| 112. #474 | D13 | semidirect |
| 206. C13 | #3358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719432 | 2 |
| #11719258 | 2 |
| C13×#474 | 2 |
| #11718749 | 2 |
| C4×#6104 | 2 |
| #11718551 | 2 |
| #11718533 | 2 |
| #11718504 | 2 |
| #11718491 | 2 |
| #11718447 | 2 |
| #11718421 | 2 |
| #3358 | 13 |