Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
584 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 584 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. C22×#92481 | C2 | semidirect |
| 3. C2×Q8×Dic31 | C2 | semidirect |
| 4. #14521247 | C2 | direct (N × H) |
| 5. C2×Dic31⋊C8 | C2 | semidirect |
| 6. C2×#11758409 | C2 | semidirect |
| 7. C2×#11758420 | C2 | semidirect |
| 8. C22×SD16×C31 | C2 | semidirect |
| 15. C2×SD16×C31 | C22 | semidirect |
| 18. Q8×Dic31 | C22 | semidirect |
| 20. C2×#92481 | C22 | semidirect |
| 28. #11758420 | C22 | semidirect |
| 29. #11758409 | C22 | semidirect |
| 30. Dic31⋊C8 | C22 | semidirect |
| 35. C2×Q8×C31 | D4 | semidirect |
| 77. Q8×C31 | C2×D4 | semidirect |
| 92. C2×Dic31 | SD16 | semidirect |
| 119. Dic31 | C2×SD16 | semidirect |
| 121. C22×SD16 | D31 | semidirect |
| 129. C2×C31 | #460 | semidirect |
| 142. C2×SD16 | C2×D31 | semidirect |
| 156. C31 | C2×#460 | semidirect |
| 161. C2×Q8 | C22⋊D31 | semidirect |
| 203. Q8 | C2×C22⋊D31 | semidirect |
| 247. C2 | #14521247 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92481 | 2 |
| C2×#11758517 | 2 |
| C2×Q8×Dic31 | 2 |
| #14521247 | 2 |
| C2×Dic31⋊C8 | 2 |
| C2×#11758409 | 2 |
| C2×#11758420 | 2 |
| C22×SD16×C31 | 2 |
| C2×#460 | 31 |