Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14521759 | C2 | semidirect |
| 3. #14521396 | C2 | semidirect |
| 4. #14521369 | C2 | semidirect |
| 5. #14521339 | C2 | semidirect |
| 6. #14521281 | C2 | semidirect |
| 7. #14521249 | C2 | semidirect |
| 8. #14521198 | C2 | semidirect |
| 9. C8×D124 | C2 | semidirect |
| 10. #102×D31 | C2 | semidirect |
| 11. C4×SD16×C31 | C2 | semidirect |
| 15. C4×Q8×C31 | C22 | semidirect |
| 17. #11758523 | C22 | semidirect |
| 18. C2×#92481 | C22 | semidirect |
| 20. C2×C8×D31 | C22 | semidirect |
| 23. C4⋊C4×D31 | C22 | semidirect |
| 29. #11758446 | C22 | semidirect |
| 30. C31×#106 | C22 | semidirect |
| 31. C31×#103 | C22 | semidirect |
| 33. C4×C8×C31 | C22 | semidirect |
| 35. #11758409 | C22 | semidirect |
| 36. #11758409 | C22 | semidirect |
| 37. (C2×D31)⋊C8 | C22 | semidirect |
| 38. #11758397 | C22 | semidirect |
| 39. #11758396 | C22 | semidirect |
| 40. C4⋊(C31⋊C8) | C22 | semidirect |
| 102. D124 | SD16 | semidirect |
| 139. C4×SD16 | D31 | semidirect |
| 161. C4×Q8 | C2×D31 | semidirect |
| 167. #106 | C2×D31 | semidirect |
| 169. #103 | 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 |
|---|---|
| #14521759 | 2 |
| D4×D124 | 2 |
| #14521396 | 2 |
| #14521369 | 2 |
| #14521339 | 2 |
| #14521281 | 2 |
| #14521249 | 2 |
| #14521198 | 2 |
| C8×D124 | 2 |
| #102×D31 | 2 |
| C4×SD16×C31 | 2 |
| #3295 | 31 |