Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 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. #14521396 | C2 | semidirect |
| 4. #14521374 | C2 | semidirect |
| 5. #14521335 | C2 | semidirect |
| 6. #14521278 | C2 | semidirect |
| 7. #14521250 | C2 | semidirect |
| 8. #14521213 | C2 | semidirect |
| 9. C4×Dic124 | C2 | semidirect |
| 10. #14521046 | C2 | semidirect |
| 11. C8×D4×C31 | C2 | semidirect |
| 132. C8×D4 | D31 | semidirect |
| 168. C31 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521769 | 2 |
| #14521720 | 2 |
| #14521396 | 2 |
| #14521374 | 2 |
| #14521335 | 2 |
| #14521278 | 2 |
| #14521250 | 2 |
| #14521213 | 2 |
| C4×Dic124 | 2 |
| #14521046 | 2 |
| C8×D4×C31 | 2 |
| #3304 | 31 |