Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1504 conjugacy classes of subgroups; only the 821 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 821 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. C2×#11758484 | C2 | direct (N × H) |
| 3. C22×#92469 | C2 | semidirect |
| 4. C23×C31⋊C8 | C2 | semidirect |
| 5. C22×C8×D31 | C2 | semidirect |
| 6. C22×M16×C31 | C2 | semidirect |
| 14. C2×M16×C31 | C22 | semidirect |
| 18. C22×C31⋊C8 | C22 | semidirect |
| 19. #11758484 | C22 | direct (N × H) |
| 20. C2×#92469 | C22 | semidirect |
| 21. C2×C8×D31 | C22 | semidirect |
| 36. M16×C31 | C23 | semidirect |
| 40. C2×C31⋊C8 | C23 | semidirect |
| 41. #92469 | C23 | semidirect |
| 42. C8×D31 | C23 | semidirect |
| 64. C22×C31 | #131 | semidirect |
| 76. C22×M16 | D31 | semidirect |
| 80. C2×C31 | C2×#131 | semidirect |
| 92. C2×M16 | C2×D31 | semidirect |
| 98. C31 | C22×#131 | semidirect |
| 114. M16 | C22×D31 | semidirect |
| 142. C22 | #11758484 | direct (N × H) |
| 151. C2 | C2×#11758484 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92495 | 2 |
| C2×#11758484 | 2 |
| C22×#92469 | 2 |
| C23×C31⋊C8 | 2 |
| C22×C8×D31 | 2 |
| C22×M16×C31 | 2 |
| C22×#131 | 31 |