Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1008 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 269 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×#11758503 | C2 | semidirect |
| 3. #14521055 | C2 | direct (N × H) |
| 4. C2×#11758409 | C2 | semidirect |
| 5. C22×M16×C31 | C2 | semidirect |
| 11. C22×D124 | C4 | semidirect |
| 15. C2×M16×C31 | C22 | semidirect |
| 16. C22×C8×C31 | C22 | semidirect |
| 19. #11758503 | C22 | semidirect |
| 20. C2×C4⋊Dic31 | C22 | semidirect |
| 22. #11758409 | C22 | semidirect |
| 42. C2×D124 | C2×C4 | semidirect |
| 46. C2×C8×C31 | C23 | semidirect |
| 49. C4⋊Dic31 | C23 | semidirect |
| 94. C22×M16 | D31 | semidirect |
| 99. C2×C31 | #418 | semidirect |
| 112. C2×M16 | C2×D31 | semidirect |
| 113. C22×C8 | C2×D31 | semidirect |
| 120. C31 | C2×#418 | semidirect |
| 144. C2×C8 | C22×D31 | semidirect |
| 192. C2 | #14521055 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D124 | 2 |
| C2×#11758503 | 2 |
| #14521055 | 2 |
| C2×#11758409 | 2 |
| C22×M16×C31 | 2 |
| C2×#418 | 31 |