Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
752 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 309 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 |
|---|---|---|
| 3. #14521058 | C2 | direct (N × H) |
| 4. C2×#11758423 | C2 | semidirect |
| 9. C22×Q8×C31 | C4 | semidirect |
| 22. #11758423 | C22 | semidirect |
| 31. C2×Q8×C31 | C2×C4 | semidirect |
| 92. C2×C31 | #419 | semidirect |
| 98. C22×Q8 | Dic31 | semidirect |
| 112. C31 | C2×#419 | semidirect |
| 121. C2×Q8 | C2×Dic31 | semidirect |
| 176. C2 | #14521058 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92474 | 2 |
| C2×#11758503 | 2 |
| #14521058 | 2 |
| C2×#11758423 | 2 |
| C23×Q8×C31 | 2 |
| C2×#419 | 31 |