Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 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. #14521771 | C2 | semidirect |
| 2. #14521442 | C2 | semidirect |
| 4. #14521271 | C2 | semidirect |
| 6. #14521258 | C2 | semidirect |
| 7. #14521179 | C2 | semidirect |
| 8. #14521148 | C2 | semidirect |
| 9. C4×Q16×C31 | C2 | semidirect |
| 107. C4×Q16 | D31 | semidirect |
| 137. C31 | #3402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521771 | 2 |
| #14521442 | 2 |
| #14521433 | 2 |
| #14521271 | 2 |
| #14521267 | 2 |
| #14521258 | 2 |
| #14521179 | 2 |
| #14521148 | 2 |
| C4×Q16×C31 | 2 |
| #3402 | 31 |