Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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. #14521772 | C2 | semidirect |
| 2. #14521759 | C2 | semidirect |
| 3. #14521404 | C2 | semidirect |
| 4. #14521400 | C2 | semidirect |
| 5. #14521357 | C2 | semidirect |
| 6. #14521340 | C2 | semidirect |
| 8. #14521255 | C2 | semidirect |
| 9. C4×#92470 | C2 | semidirect |
| 11. C8×Q8×C31 | C2 | semidirect |
| 124. C8×Q8 | D31 | semidirect |
| 161. C31 | #3360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521772 | 2 |
| #14521759 | 2 |
| #14521404 | 2 |
| #14521400 | 2 |
| #14521357 | 2 |
| #14521340 | 2 |
| #14521265 | 2 |
| #14521255 | 2 |
| C4×#92470 | 2 |
| C4×D248 | 2 |
| C8×Q8×C31 | 2 |
| #3360 | 31 |