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 |
| 2. #14521408 | C2 | semidirect |
| 3. #14521403 | C2 | semidirect |
| 4. #14521058 | C2 | semidirect |
| 6. C4×#92474 | C2 | semidirect |
| 18. #11758447 | C22 | semidirect |
| 19. #11758446 | C22 | semidirect |
| 21. #11758423 | C22 | semidirect |
| 23. #11758391 | C22 | semidirect |
| 24. C4×C31⋊C8 | C22 | 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 |
| #14521408 | 2 |
| #14521403 | 2 |
| #14521058 | 2 |
| #14521054 | 2 |
| C4×#92474 | 2 |
| C2×C31×#124 | 2 |
| #3140 | 31 |