Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. C2×#11758403 | C2 | semidirect |
| 5. #14520804 | C2 | semidirect |
| 6. #14520803 | C2 | semidirect |
| 7. C2×C4×C8×C31 | C2 | semidirect |
| 18. C2×#92469 | C4 | semidirect |
| 21. (C2×D31)⋊C8 | C4 | semidirect |
| 60. C2×C4×C31 | M16 | semidirect |
| 78. C8×C31 | C22⋊C4 | semidirect |
| 102. C2×C4×C8 | D31 | semidirect |
| 127. C31 | #1753 | semidirect |
| 175. C2×C4 | #92469 | semidirect |
| 185. C8 | (C2×D31)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92469 | 2 |
| C2×(C2×D31)⋊C8 | 2 |
| C2×#11758403 | 2 |
| C4×(C2×D31)⋊C4 | 2 |
| #14520804 | 2 |
| #14520803 | 2 |
| C2×C4×C8×C31 | 2 |
| #1753 | 31 |