Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #14521400 | C2 | semidirect |
| 4. #14521385 | C2 | semidirect |
| 5. #14521345 | C2 | semidirect |
| 6. #14521290 | C2 | semidirect |
| 7. #14521260 | C2 | semidirect |
| 8. #14521207 | C2 | semidirect |
| 9. C4×Dic124 | C2 | semidirect |
| 10. C2×#11758404 | C2 | semidirect |
| 77. D4×C31 | Q16 | semidirect |
| 163. C31 | #3299 | semidirect |
| 208. D4 | Dic124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521756 | 2 |
| D4×Dic62 | 2 |
| #14521400 | 2 |
| #14521385 | 2 |
| #14521345 | 2 |
| #14521290 | 2 |
| #14521260 | 2 |
| #14521207 | 2 |
| C4×Dic124 | 2 |
| C2×#11758404 | 2 |
| C8×D4×C31 | 2 |
| #3299 | 31 |