Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14521760 | C2 | semidirect |
| 3. #14521366 | C2 | semidirect |
| 4. #14521336 | C2 | semidirect |
| 5. #14521277 | C2 | semidirect |
| 6. #14521246 | C2 | semidirect |
| 7. #14521201 | C2 | semidirect |
| 8. C4×#92470 | C2 | semidirect |
| 9. C8×D124 | C2 | semidirect |
| 10. #102×D31 | C2 | semidirect |
| 11. C31×#486 | C2 | semidirect |
| 14. C31×C4⋊Q8 | C22 | semidirect |
| 20. C2×#92480 | C22 | semidirect |
| 22. C2×C8×D31 | C22 | semidirect |
| 23. #11758474 | C22 | semidirect |
| 25. C4⋊C4×D31 | C22 | semidirect |
| 29. C4×Dic62 | C22 | semidirect |
| 30. C31×#102 | C22 | semidirect |
| 31. C31×#102 | C22 | semidirect |
| 32. C4×C8×C31 | C22 | semidirect |
| 33. #11758420 | C22 | semidirect |
| 35. (C2×D31)⋊C8 | C22 | semidirect |
| 36. #11758405 | C22 | semidirect |
| 37. #11758404 | C22 | semidirect |
| 39. #11758396 | C22 | semidirect |
| 40. C4⋊(C31⋊C8) | C22 | semidirect |
| 99. D124 | SD16 | semidirect |
| 133. #486 | D31 | semidirect |
| 153. C4⋊Q8 | C2×D31 | semidirect |
| 173. #102 | C2×D31 | semidirect |
| 174. #102 | C2×D31 | semidirect |
| 176. C4×C8 | C2×D31 | semidirect |
| 177. C31 | #3295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521760 | 2 |
| #14521684 | 2 |
| #14521366 | 2 |
| #14521336 | 2 |
| #14521277 | 2 |
| #14521246 | 2 |
| #14521201 | 2 |
| C4×#92470 | 2 |
| C8×D124 | 2 |
| #102×D31 | 2 |
| C31×#486 | 2 |
| #3295 | 31 |