Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14521862 | C2 | semidirect |
| 2. #14521491 | C2 | semidirect |
| 3. #14521490 | C2 | semidirect |
| 4. #14521482 | C2 | semidirect |
| 5. #14521481 | C2 | semidirect |
| 6. Q32×D31 | C2 | semidirect |
| 7. #14521465 | C2 | semidirect |
| 8. C2×C31×Q32 | C2 | semidirect |
| 84. C2×Q32 | D31 | semidirect |
| 109. C31 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521862 | 2 |
| #14521491 | 2 |
| #14521490 | 2 |
| #14521482 | 2 |
| #14521481 | 2 |
| Q32×D31 | 2 |
| #14521465 | 2 |
| C2×C31×Q32 | 2 |
| #3417 | 31 |