Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 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. C22×#92482 | C2 | semidirect |
| 3. #14521428 | C2 | semidirect |
| 4. #14521288 | C2 | semidirect |
| 5. #14521259 | C2 | semidirect |
| 6. #14521256 | C2 | semidirect |
| 7. #14521205 | C2 | semidirect |
| 8. #14521204 | C2 | semidirect |
| 9. C4×#92482 | C2 | semidirect |
| 71. #92482 | D4 | direct (N × H) |
| 88. D4×C31 | Q16 | semidirect |
| 114. C22×C31 | C2×Q16 | semidirect |
| 121. C4×C31 | C2×Q16 | semidirect |
| 172. C31 | D4×Q16 | semidirect |
| 224. D4 | #92482 | direct (N × H) |
| 244. C22 | C2×#92482 | semidirect |
| 254. C4 | C2×#92482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92482 | 2 |
| D4×Dic62 | 2 |
| #14521428 | 2 |
| #14521288 | 2 |
| #14521259 | 2 |
| #14521256 | 2 |
| #14521205 | 2 |
| #14521204 | 2 |
| C4×#92482 | 2 |
| D4×C31⋊C8 | 2 |
| D4×Q8×C31 | 2 |
| D4×Q16 | 31 |