Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11758564 | C2 | semidirect |
| 2. C2×#11758519 | C2 | semidirect |
| 3. C2×#11758481 | C2 | semidirect |
| 4. #14521630 | C2 | semidirect |
| 5. #14521214 | C2 | semidirect |
| 6. #14521206 | C2 | semidirect |
| 7. #14521197 | C2 | semidirect |
| 8. #14521189 | C2 | semidirect |
| 9. #14521048 | C2 | semidirect |
| 10. #14521015 | C2 | semidirect |
| 11. C2×C31×#103 | C2 | semidirect |
| 47. C2×Q8×C31 | D4 | semidirect |
| 67. #92495 | D4 | semidirect |
| 172. C2×#103 | D31 | semidirect |
| 214. C31 | #3013 | semidirect |
| 234. C2×Q8 | D124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758564 | 2 |
| C2×#11758519 | 2 |
| C2×#11758481 | 2 |
| #14521630 | 2 |
| #14521214 | 2 |
| #14521206 | 2 |
| #14521197 | 2 |
| #14521189 | 2 |
| #14521048 | 2 |
| #14521015 | 2 |
| C2×C31×#103 | 2 |
| #3013 | 31 |