Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #14521600 | C2 | semidirect |
| 2. C4×#92499 | C2 | semidirect |
| 3. #14521375 | C2 | semidirect |
| 4. #14521326 | C2 | semidirect |
| 5. #14521249 | C2 | semidirect |
| 6. #14521245 | C2 | semidirect |
| 7. #14521197 | C2 | semidirect |
| 8. #14521160 | C2 | semidirect |
| 9. #14521152 | C2 | semidirect |
| 10. #14521105 | C2 | semidirect |
| 11. C31×#475 | C2 | semidirect |
| 88. Q8×C31 | #41 | semidirect |
| 106. D124 | #41 | semidirect |
| 142. #475 | D31 | semidirect |
| 187. C31 | #3115 | semidirect |
| 233. Q8 | #92499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521600 | 2 |
| C4×#92499 | 2 |
| #14521375 | 2 |
| #14521326 | 2 |
| #14521249 | 2 |
| #14521245 | 2 |
| #14521197 | 2 |
| #14521160 | 2 |
| #14521152 | 2 |
| #14521105 | 2 |
| C31×#475 | 2 |
| #3115 | 31 |