Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 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. #14521702 | C2 | semidirect |
| 2. #14521684 | C2 | semidirect |
| 3. #14521361 | C2 | semidirect |
| 4. #14521326 | C2 | semidirect |
| 5. #14521284 | C2 | semidirect |
| 6. #14521241 | C2 | semidirect |
| 7. #14521184 | C2 | semidirect |
| 8. C4×D248 | C2 | semidirect |
| 9. C8×D124 | C2 | semidirect |
| 10. #102×D31 | C2 | semidirect |
| 11. C31×#486 | C2 | semidirect |
| 15. C31×C4⋊Q8 | C22 | semidirect |
| 21. C2×#92479 | C22 | semidirect |
| 23. C2×C8×D31 | C22 | semidirect |
| 24. #11758472 | C22 | semidirect |
| 26. C4⋊C4×D31 | C22 | semidirect |
| 29. C4×D124 | C22 | semidirect |
| 30. C31×#102 | C22 | semidirect |
| 31. C31×#102 | C22 | semidirect |
| 32. C4×C8×C31 | C22 | semidirect |
| 33. #11758420 | C22 | semidirect |
| 35. #11758409 | C22 | semidirect |
| 36. (C2×D31)⋊C8 | C22 | semidirect |
| 37. #11758406 | C22 | semidirect |
| 39. #11758395 | C22 | semidirect |
| 40. C4⋊(C31⋊C8) | C22 | semidirect |
| 103. D124 | D8 | semidirect |
| 104. D124 | #41 | semidirect |
| 138. #486 | D31 | semidirect |
| 160. C4⋊Q8 | C2×D31 | semidirect |
| 179. #102 | C2×D31 | semidirect |
| 180. #102 | C2×D31 | semidirect |
| 182. C4×C8 | C2×D31 | semidirect |
| 183. C31 | #3294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521702 | 2 |
| #14521684 | 2 |
| #14521361 | 2 |
| #14521326 | 2 |
| #14521284 | 2 |
| #14521241 | 2 |
| #14521184 | 2 |
| C4×D248 | 2 |
| C8×D124 | 2 |
| #102×D31 | 2 |
| C31×#486 | 2 |
| #3294 | 31 |