Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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×#92469 | C2 | semidirect |
| 3. C2×#11758409 | C2 | semidirect |
| 4. C2×#11758397 | C2 | semidirect |
| 5. #14520906 | C2 | semidirect |
| 6. #14520811 | C2 | semidirect |
| 7. C31×#340 | C2 | semidirect |
| 22. #11758472 | C4 | semidirect |
| 50. C2×C8×C31 | D4 | semidirect |
| 61. C2×C31⋊C8 | D4 | semidirect |
| 143. #340 | D31 | semidirect |
| 171. C31 | #1895 | semidirect |
| 200. C2×C8 | D124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92469 | 2 |
| C2×#11758472 | 2 |
| C2×#11758409 | 2 |
| C2×#11758397 | 2 |
| #14520906 | 2 |
| #14520811 | 2 |
| C31×#340 | 2 |
| #1895 | 31 |