Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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. #14521399 | C2 | semidirect |
| 3. #14521382 | C2 | semidirect |
| 4. #14521344 | C2 | semidirect |
| 5. #14521288 | C2 | semidirect |
| 6. #14521256 | C2 | semidirect |
| 7. #14521205 | C2 | semidirect |
| 8. C4×#92482 | C2 | semidirect |
| 10. C2×#11758423 | C2 | semidirect |
| 82. D4×C31 | Q16 | semidirect |
| 163. C31 | #3299 | semidirect |
| 208. D4 | #92482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521756 | 2 |
| #14521399 | 2 |
| #14521382 | 2 |
| #14521344 | 2 |
| #14521288 | 2 |
| #14521256 | 2 |
| #14521205 | 2 |
| C4×#92482 | 2 |
| D4×C31⋊C8 | 2 |
| C2×#11758423 | 2 |
| D4×Q8×C31 | 2 |
| #3299 | 31 |