Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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×Q16×D31 | C2 | semidirect |
| 3. #14521491 | C2 | direct (N × H) |
| 4. C2×#11758417 | C2 | semidirect |
| 5. C2×#11758388 | C2 | semidirect |
| 6. C2×#11758416 | C2 | semidirect |
| 7. C2×#11758386 | C2 | semidirect |
| 8. C2×C31×Q32 | C2 | semidirect |
| 18. Q16×D31 | C22 | semidirect |
| 22. C31×Q32 | C22 | semidirect |
| 24. #11758417 | C22 | semidirect |
| 25. #11758416 | C22 | semidirect |
| 27. #11758388 | C22 | semidirect |
| 28. #11758386 | C22 | semidirect |
| 98. C2×Q32 | D31 | semidirect |
| 102. C2×C31 | #510 | semidirect |
| 120. Q32 | C2×D31 | semidirect |
| 126. C31 | C2×#510 | semidirect |
| 193. C2 | #14521491 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758496 | 2 |
| C2×Q16×D31 | 2 |
| #14521491 | 2 |
| C2×#11758417 | 2 |
| C2×#11758388 | 2 |
| C2×#11758416 | 2 |
| C2×#11758386 | 2 |
| C2×C31×Q32 | 2 |
| C2×#510 | 31 |