Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. Q8×Dic62 | C2 | semidirect |
| 3. #14521396 | C2 | semidirect |
| 4. #14521394 | C2 | semidirect |
| 5. #14521339 | C2 | semidirect |
| 6. #14521338 | C2 | semidirect |
| 7. #14521249 | C2 | semidirect |
| 8. #14521247 | C2 | semidirect |
| 9. C8×Dic62 | C2 | semidirect |
| 10. #14521134 | C2 | semidirect |
| 11. C4×SD16×C31 | C2 | semidirect |
| 77. Q8×C31 | #41 | semidirect |
| 99. Dic62 | SD16 | semidirect |
| 131. C4×SD16 | D31 | semidirect |
| 166. C31 | #3362 | semidirect |
| 206. Q8 | #92495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic62 | 2 |
| #14521720 | 2 |
| #14521396 | 2 |
| #14521394 | 2 |
| #14521339 | 2 |
| #14521338 | 2 |
| #14521249 | 2 |
| #14521247 | 2 |
| C8×Dic62 | 2 |
| #14521134 | 2 |
| C4×SD16×C31 | 2 |
| #3362 | 31 |