Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 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. #14521720 | C2 | semidirect |
| 2. D4×Dic62 | C2 | semidirect |
| 3. #14521396 | C2 | semidirect |
| 4. #14521394 | C2 | semidirect |
| 5. #14521329 | C2 | semidirect |
| 6. #14521328 | C2 | semidirect |
| 7. #14521244 | C2 | semidirect |
| 8. #14521242 | C2 | semidirect |
| 9. C8×Dic62 | C2 | semidirect |
| 10. #14521129 | C2 | semidirect |
| 11. C4×D8×C31 | C2 | semidirect |
| 81. D4×C31 | #41 | semidirect |
| 102. Dic62 | D8 | semidirect |
| 136. C4×D8 | D31 | semidirect |
| 172. C31 | #3358 | semidirect |
| 222. D4 | #92495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521720 | 2 |
| D4×Dic62 | 2 |
| #14521396 | 2 |
| #14521394 | 2 |
| #14521329 | 2 |
| #14521328 | 2 |
| #14521244 | 2 |
| #14521242 | 2 |
| C8×Dic62 | 2 |
| #14521129 | 2 |
| C4×D8×C31 | 2 |
| #3358 | 31 |