Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×#11758496 | C2 | semidirect |
| 2. C2×Q16×D31 | C2 | semidirect |
| 3. #14521711 | C2 | semidirect |
| 4. #14521433 | C2 | semidirect |
| 5. #14521291 | C2 | semidirect |
| 6. #14521286 | C2 | semidirect |
| 7. #14521271 | C2 | semidirect |
| 8. #14521214 | C2 | semidirect |
| 9. #14521189 | C2 | semidirect |
| 10. C8×D124 | C2 | semidirect |
| 11. C4×Q16×C31 | C2 | semidirect |
| 56. Q16×C31 | D4 | semidirect |
| 121. C2×D31 | #135 | semidirect |
| 140. C4×Q16 | D31 | semidirect |
| 177. C31 | #3285 | semidirect |
| 195. Q16 | D124 | semidirect |
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 |
| #14521711 | 2 |
| #14521433 | 2 |
| #14521291 | 2 |
| #14521286 | 2 |
| #14521271 | 2 |
| #14521214 | 2 |
| #14521189 | 2 |
| C8×D124 | 2 |
| C4×Q16×C31 | 2 |
| #3285 | 31 |