Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14521769 | C2 | semidirect |
| 3. #14521400 | C2 | semidirect |
| 4. #14521391 | C2 | semidirect |
| 5. #14521330 | C2 | semidirect |
| 6. #14521290 | C2 | semidirect |
| 7. #14521260 | C2 | semidirect |
| 8. #14521213 | C2 | semidirect |
| 9. C4×#92470 | C2 | semidirect |
| 10. #14521046 | C2 | semidirect |
| 11. C8×D4×C31 | C2 | semidirect |
| 130. C8×D4 | D31 | semidirect |
| 166. C31 | #3302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521769 | 2 |
| #14521704 | 2 |
| #14521400 | 2 |
| #14521391 | 2 |
| #14521330 | 2 |
| #14521290 | 2 |
| #14521260 | 2 |
| #14521213 | 2 |
| C4×#92470 | 2 |
| #14521046 | 2 |
| C8×D4×C31 | 2 |
| #3302 | 31 |