Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14521606 | C2 | semidirect |
| 3. #14521409 | C2 | semidirect |
| 4. #14521404 | C2 | semidirect |
| 5. #14521059 | C2 | semidirect |
| 7. C4×M16×C31 | C2 | semidirect |
| 18. #11758447 | C22 | semidirect |
| 19. #11758446 | C22 | semidirect |
| 21. C31×#97 | C22 | semidirect |
| 22. C4×C8×C31 | C22 | semidirect |
| 24. #11758404 | C22 | semidirect |
| 86. C4×M16 | D31 | semidirect |
| 106. #97 | C2×D31 | semidirect |
| 107. C4×C8 | C2×D31 | semidirect |
| 108. C31 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521606 | 2 |
| C2×#11758452 | 2 |
| #14521409 | 2 |
| #14521404 | 2 |
| #14521059 | 2 |
| #14521055 | 2 |
| C4×M16×C31 | 2 |
| #3140 | 31 |