Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#11758484 | C2 | semidirect |
| 2. C22×#92469 | C2 | semidirect |
| 4. #14521126 | C2 | semidirect |
| 5. #14521119 | C2 | semidirect |
| 6. #14521015 | C2 | semidirect |
| 7. #14521012 | C2 | semidirect |
| 8. #14521005 | C2 | semidirect |
| 9. C31×#424 | C2 | semidirect |
| 21. C2×#92469 | C22 | semidirect |
| 22. C2×C8×D31 | C22 | semidirect |
| 28. C31×C4⋊C8 | C22 | semidirect |
| 30. (C2×D31)⋊C8 | C22 | semidirect |
| 31. #11758391 | C22 | semidirect |
| 32. C4×C31⋊C8 | C22 | semidirect |
| 58. C2×C31⋊C8 | D4 | semidirect |
| 114. #424 | D31 | semidirect |
| 141. C4⋊C8 | C2×D31 | semidirect |
| 146. C31 | #2930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758484 | 2 |
| C22×#92469 | 2 |
| #14521561 | 2 |
| #14521126 | 2 |
| #14521119 | 2 |
| #14521015 | 2 |
| #14521012 | 2 |
| #14521005 | 2 |
| C31×#424 | 2 |
| #2930 | 31 |