Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×Q16×D31 | C2 | semidirect |
| 4. #14521428 | C2 | semidirect |
| 5. #14521289 | C2 | semidirect |
| 6. #14521260 | C2 | semidirect |
| 7. #14521206 | C2 | semidirect |
| 8. #14521203 | C2 | semidirect |
| 9. C4×#92482 | C2 | semidirect |
| 11. C31×#462 | C2 | semidirect |
| 66. #92482 | D4 | semidirect |
| 97. D124 | Q16 | semidirect |
| 115. C2×D31 | C2×Q16 | semidirect |
| 120. C4×C31 | C2×Q16 | semidirect |
| 133. #462 | D31 | semidirect |
| 172. C31 | D4×Q16 | semidirect |
| 254. C4 | Q16×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D31 | 2 |
| Q8×D124 | 2 |
| #14521714 | 2 |
| #14521428 | 2 |
| #14521289 | 2 |
| #14521260 | 2 |
| #14521206 | 2 |
| #14521203 | 2 |
| C4×#92482 | 2 |
| #14521114 | 2 |
| C31×#462 | 2 |
| D4×Q16 | 31 |