Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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×#11758493 | C2 | semidirect |
| 2. #14521721 | C2 | semidirect |
| 3. #14521719 | C2 | semidirect |
| 4. #14521425 | C2 | semidirect |
| 5. #14521284 | C2 | semidirect |
| 6. #14521250 | C2 | semidirect |
| 7. #14521195 | C2 | semidirect |
| 8. #14521193 | C2 | semidirect |
| 9. C4×#92482 | C2 | semidirect |
| 10. #14521114 | C2 | semidirect |
| 11. C31×#460 | C2 | semidirect |
| 69. #92482 | D4 | semidirect |
| 131. C4×C31 | #135 | semidirect |
| 143. #460 | D31 | semidirect |
| 184. C31 | #3287 | semidirect |
| 276. C4 | #11758493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758493 | 2 |
| #14521721 | 2 |
| #14521719 | 2 |
| #14521425 | 2 |
| #14521284 | 2 |
| #14521250 | 2 |
| #14521195 | 2 |
| #14521193 | 2 |
| C4×#92482 | 2 |
| #14521114 | 2 |
| C31×#460 | 2 |
| #3287 | 31 |