Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #11719530 | C2 | semidirect |
| 3. #11719503 | C2 | semidirect |
| 4. C22×#6105 | C2 | semidirect |
| 5. #11718894 | C2 | semidirect |
| 6. #11718823 | C2 | semidirect |
| 7. #11718814 | C2 | semidirect |
| 8. #11718781 | C2 | semidirect |
| 9. #11718780 | C2 | semidirect |
| 18. #88198 | C22 | semidirect |
| 19. #88190 | C22 | semidirect |
| 29. #88075 | C22 | semidirect |
| 30. #88072 | C22 | semidirect |
| 31. #88056 | C22 | semidirect |
| 32. #88054 | C22 | semidirect |
| 183. C13 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×AGL(1,ℤ/8) | 2 |
| #11719530 | 2 |
| #11719503 | 2 |
| C22×#6105 | 2 |
| #11718894 | 2 |
| #11718823 | 2 |
| #11718814 | 2 |
| #11718781 | 2 |
| #11718780 | 2 |
| #3042 | 13 |