Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#11758485 | C2 | semidirect |
| 2. C2×#11758527 | C2 | semidirect |
| 3. C22×#92479 | C2 | semidirect |
| 4. #14521616 | C2 | semidirect |
| 5. #14521613 | C2 | semidirect |
| 6. #14521437 | C2 | semidirect |
| 7. #14521435 | C2 | semidirect |
| 8. #14521430 | C2 | semidirect |
| 9. #14521424 | C2 | semidirect |
| 10. #14521007 | C2 | semidirect |
| 11. C2×C31×AGL(1,ℤ/8) | C2 | semidirect |
| 17. C2×SD16×C31 | C22 | semidirect |
| 18. C2×D8×C31 | C22 | semidirect |
| 22. #11758524 | C22 | semidirect |
| 23. C2×#92482 | C22 | semidirect |
| 24. C2×#92481 | C22 | semidirect |
| 25. #11758517 | C22 | semidirect |
| 26. #11758517 | C22 | semidirect |
| 29. #11758513 | C22 | semidirect |
| 30. C2×#92480 | C22 | semidirect |
| 34. C2×#92479 | C22 | semidirect |
| 39. C2×D248 | C22 | semidirect |
| 40. C2×#92470 | C22 | semidirect |
| 41. #11758403 | C22 | semidirect |
| 42. C8×Dic31 | C22 | semidirect |
| 70. M16×C31 | D4 | semidirect |
| 83. C2×C31⋊C8 | D4 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D31 | semidirect |
| 176. C2×SD16 | C2×D31 | semidirect |
| 182. C2×D8 | C2×D31 | semidirect |
| 196. C31 | #3155 | semidirect |
| 232. M16 | C22⋊D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758485 | 2 |
| C2×#11758527 | 2 |
| C22×#92479 | 2 |
| #14521616 | 2 |
| #14521613 | 2 |
| #14521437 | 2 |
| #14521435 | 2 |
| #14521430 | 2 |
| #14521424 | 2 |
| #14521007 | 2 |
| C2×C31×AGL(1,ℤ/8) | 2 |
| #3155 | 31 |