Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
656 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 165 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×SD16×D31 | C2 | semidirect |
| 2. C4⋊Q8×D31 | C2 | semidirect |
| 4. #14521423 | C2 | semidirect |
| 5. #14521422 | C2 | semidirect |
| 6. #14521421 | C2 | semidirect |
| 7. #14521420 | C2 | semidirect |
| 8. C4×C8×D31 | C2 | semidirect |
| 9. C31×#492 | C2 | semidirect |
| 13. C2×SD16×C31 | C22 | semidirect |
| 14. C31×C4⋊Q8 | C22 | semidirect |
| 16. #11758521 | C22 | semidirect |
| 17. C2×#92481 | C22 | semidirect |
| 20. C2×#92480 | C22 | semidirect |
| 22. C2×#92470 | C22 | semidirect |
| 28. #11758446 | C22 | semidirect |
| 29. C4×C8×C31 | C22 | semidirect |
| 30. C8×Dic31 | C22 | semidirect |
| 31. C4×C31⋊C8 | C22 | semidirect |
| 60. C8×D31 | D4 | semidirect |
| 80. C4×D31 | SD16 | semidirect |
| 84. C8×C31 | C2×D4 | semidirect |
| 85. C31⋊C8 | C2×D4 | semidirect |
| 96. C4×C31 | C2×SD16 | semidirect |
| 100. Dic31 | C2×SD16 | semidirect |
| 108. #492 | D31 | direct (N × H) |
| 114. D31 | #492 | direct (N × H) |
| 122. C2×SD16 | C2×D31 | semidirect |
| 127. C4⋊Q8 | C2×D31 | semidirect |
| 136. C4×C8 | C2×D31 | semidirect |
| 137. C31 | C2×#492 | semidirect |
| 191. C8 | D4×D31 | semidirect |
| 204. C4 | SD16×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×D31 | 2 |
| C4⋊Q8×D31 | 2 |
| #127×D31 | 2 |
| #14521423 | 2 |
| #14521422 | 2 |
| #14521421 | 2 |
| #14521420 | 2 |
| C4×C8×D31 | 2 |
| C31×#492 | 2 |
| C2×#492 | 31 |