Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. #14521397 | C2 | semidirect |
| 3. #14521367 | C2 | semidirect |
| 4. #14521336 | C2 | semidirect |
| 5. #14521280 | C2 | semidirect |
| 6. #14521249 | C2 | semidirect |
| 7. #14521199 | C2 | semidirect |
| 8. C4×#92481 | C2 | semidirect |
| 9. D4×C31⋊C8 | C2 | semidirect |
| 10. C2×#11758397 | C2 | semidirect |
| 11. C31×#554 | C2 | semidirect |
| 14. C31×C4⋊Q8 | C22 | semidirect |
| 17. C31×C22⋊Q8 | C22 | semidirect |
| 18. C4×Q8×C31 | C22 | semidirect |
| 21. C2×C4⋊C4×C31 | C22 | semidirect |
| 23. C2×#92481 | C22 | semidirect |
| 25. C22×C31⋊C8 | C22 | semidirect |
| 30. #11758423 | C22 | semidirect |
| 31. C22⋊(C31⋊C8) | C22 | semidirect |
| 34. #11758397 | C22 | semidirect |
| 35. #11758397 | C22 | semidirect |
| 36. #11758397 | C22 | semidirect |
| 37. #11758396 | C22 | semidirect |
| 38. #11758396 | C22 | semidirect |
| 39. C4⋊(C31⋊C8) | C22 | semidirect |
| 40. C4×C31⋊C8 | C22 | semidirect |
| 86. D4×C31 | SD16 | semidirect |
| 131. #554 | D31 | semidirect |
| 153. C4⋊Q8 | C2×D31 | semidirect |
| 157. C22⋊Q8 | C2×D31 | semidirect |
| 161. C4×Q8 | C2×D31 | semidirect |
| 165. C2×C4⋊C4 | C2×D31 | semidirect |
| 177. C31 | #3295 | semidirect |
| 231. D4 | #92481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D124 | 2 |
| #14521397 | 2 |
| #14521367 | 2 |
| #14521336 | 2 |
| #14521280 | 2 |
| #14521249 | 2 |
| #14521199 | 2 |
| C4×#92481 | 2 |
| D4×C31⋊C8 | 2 |
| C2×#11758397 | 2 |
| C31×#554 | 2 |
| #3295 | 31 |