Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14521447 | C2 | semidirect |
| 4. #14521388 | C2 | semidirect |
| 5. #14521378 | C2 | semidirect |
| 6. #14521344 | C2 | semidirect |
| 7. #14521334 | C2 | semidirect |
| 8. #14521304 | C2 | semidirect |
| 10. #14521090 | C2 | semidirect |
| 11. C4×Q16×C31 | C2 | semidirect |
| 121. C4×Q16 | D31 | semidirect |
| 157. C31 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521772 | 2 |
| #14521759 | 2 |
| #14521447 | 2 |
| #14521388 | 2 |
| #14521378 | 2 |
| #14521344 | 2 |
| #14521334 | 2 |
| #14521304 | 2 |
| #14521128 | 2 |
| #14521090 | 2 |
| C4×Q16×C31 | 2 |
| #3356 | 31 |