Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #14521147 | C2 | semidirect |
| 4. C4×#92481 | C2 | semidirect |
| 5. #14521085 | C2 | semidirect |
| 6. #14521058 | C2 | semidirect |
| 8. #14521005 | C2 | semidirect |
| 9. C31×#519 | C2 | semidirect |
| 13. C4×Q8×C31 | C22 | semidirect |
| 17. C2×#92481 | C4 | semidirect |
| 26. #11758423 | C22 | semidirect |
| 28. #11758396 | C22 | semidirect |
| 29. #11758395 | C22 | semidirect |
| 30. #11758391 | C22 | semidirect |
| 31. C4×C31⋊C8 | C22 | semidirect |
| 35. C2×Q8×C31 | C2×C4 | semidirect |
| 53. #92481 | C2×C4 | semidirect |
| 54. #92481 | C2×C4 | semidirect |
| 59. C2×C31⋊C8 | C2×C4 | semidirect |
| 101. #519 | D31 | semidirect |
| 121. C4×Q8 | C2×D31 | semidirect |
| 135. C31 | #2949 | semidirect |
| 139. C2×Q8 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92481 | 2 |
| #14521523 | 2 |
| #14521147 | 2 |
| C4×#92481 | 2 |
| #14521085 | 2 |
| #14521058 | 2 |
| #14521053 | 2 |
| #14521005 | 2 |
| C31×#519 | 2 |
| #2949 | 31 |