Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #14521457 | C2 | semidirect |
| 4. #14521456 | C2 | semidirect |
| 5. #14521451 | C2 | semidirect |
| 6. #14521448 | C2 | semidirect |
| 7. #14521448 | C2 | semidirect |
| 11. C31×#499 | C2 | semidirect |
| 64. #92469 | Q8 | semidirect |
| 65. #92469 | Q8 | semidirect |
| 104. #499 | D31 | semidirect |
| 138. C31 | #3166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521605 | 2 |
| #125×D31 | 2 |
| #14521457 | 2 |
| #14521456 | 2 |
| #14521451 | 2 |
| #14521448 | 2 |
| #14521090 | 2 |
| #14521088 | 2 |
| C4×#92469 | 2 |
| C31×#499 | 2 |
| #3166 | 31 |