Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
432 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 432 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 |
|---|---|---|
| 2. C2×#11758409 | C2 | semidirect |
| 3. #14520909 | C2 | semidirect |
| 4. #14520812 | C2 | semidirect |
| 5. C23×C8×C31 | C2 | semidirect |
| 14. #11758507 | C4 | semidirect |
| 40. C2×C8×C31 | D4 | semidirect |
| 83. C22×C31 | #102 | semidirect |
| 100. C23×C8 | D31 | semidirect |
| 126. C31 | #1893 | semidirect |
| 147. C2×C8 | C22⋊D31 | semidirect |
| 194. C22 | #11758409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758507 | 2 |
| C2×#11758409 | 2 |
| #14520909 | 2 |
| #14520812 | 2 |
| C23×C8×C31 | 2 |
| #1893 | 31 |