Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#11758481 | C2 | semidirect |
| 2. #14521720 | C2 | semidirect |
| 3. #14521426 | C2 | semidirect |
| 4. #14521285 | C2 | semidirect |
| 5. #14521250 | C2 | semidirect |
| 6. #14521196 | C2 | semidirect |
| 7. C4×Dic124 | C2 | semidirect |
| 8. C8×D4×C31 | C2 | semidirect |
| 51. Dic124 | D4 | semidirect |
| 88. C4×C31 | #135 | semidirect |
| 100. C8×D4 | D31 | semidirect |
| 126. C31 | #3287 | semidirect |
| 187. C4 | #11758481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758481 | 2 |
| #14521720 | 2 |
| #14521426 | 2 |
| #14521285 | 2 |
| #14521250 | 2 |
| #14521196 | 2 |
| C4×Dic124 | 2 |
| C8×D4×C31 | 2 |
| #3287 | 31 |