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. #14521719 | C2 | semidirect |
| 2. D4×Dic62 | C2 | semidirect |
| 3. #14521395 | C2 | semidirect |
| 4. #14521394 | C2 | semidirect |
| 5. #14521330 | C2 | semidirect |
| 6. #14521327 | C2 | semidirect |
| 7. #14521242 | C2 | semidirect |
| 8. #14521173 | C2 | semidirect |
| 9. D8×Dic31 | C2 | semidirect |
| 10. C4×#92479 | C2 | semidirect |
| 11. C31×#459 | C2 | semidirect |
| 83. D4×C31 | #41 | semidirect |
| 102. Dic62 | D8 | semidirect |
| 133. #459 | D31 | semidirect |
| 172. C31 | #3358 | semidirect |
| 222. D4 | #92497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521719 | 2 |
| D4×Dic62 | 2 |
| #14521395 | 2 |
| #14521394 | 2 |
| #14521330 | 2 |
| #14521327 | 2 |
| #14521242 | 2 |
| #14521173 | 2 |
| D8×Dic31 | 2 |
| C4×#92479 | 2 |
| C31×#459 | 2 |
| #3358 | 31 |