Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 2. #14521816 | C2 | semidirect |
| 3. #14521067 | C2 | semidirect |
| 4. C2×#11758393 | C2 | semidirect |
| 5. C4×#41×C31 | C2 | semidirect |
| 7. #11758567 | C4 | semidirect |
| 8. #11758566 | C4 | semidirect |
| 15. C31×#117 | C22 | semidirect |
| 16. C2×C42×C31 | C22 | semidirect |
| 18. C2×#92474 | C22 | semidirect |
| 19. #11758393 | C22 | semidirect |
| 20. #11758393 | C22 | semidirect |
| 34. #92495 | C2×C4 | semidirect |
| 36. C2×D124 | C2×C4 | semidirect |
| 38. C2×Dic62 | C2×C4 | semidirect |
| 82. C4×#41 | D31 | semidirect |
| 100. #117 | C2×D31 | semidirect |
| 101. C2×C42 | C2×D31 | semidirect |
| 104. C31 | #2901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521885 | 2 |
| #14521816 | 2 |
| #14521067 | 2 |
| C2×#11758393 | 2 |
| C4×#41×C31 | 2 |
| #2901 | 31 |