Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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. C22×#92470 | C2 | semidirect |
| 3. C2×#11758513 | C2 | semidirect |
| 4. C2×#11758470 | C2 | semidirect |
| 5. #14521263 | C2 | direct (N × H) |
| 6. C2×Dic31⋊C8 | C2 | semidirect |
| 7. C2×#11758398 | C2 | semidirect |
| 8. C2×C31×#102 | C2 | semidirect |
| 18. #11758513 | C22 | semidirect |
| 25. C2×#92470 | C22 | semidirect |
| 27. #11758470 | C22 | semidirect |
| 28. C31×#102 | C22 | semidirect |
| 29. Dic31⋊C8 | C22 | semidirect |
| 30. #11758398 | C22 | semidirect |
| 125. C2×#102 | D31 | semidirect |
| 127. C2×C31 | #463 | semidirect |
| 153. #102 | C2×D31 | semidirect |
| 154. C31 | C2×#463 | semidirect |
| 243. C2 | #14521263 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92470 | 2 |
| C22×#92479 | 2 |
| C2×#11758513 | 2 |
| C2×#11758470 | 2 |
| #14521263 | 2 |
| C2×Dic31⋊C8 | 2 |
| C2×#11758398 | 2 |
| C2×C31×#102 | 2 |
| C2×#463 | 31 |