Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #14521346 | C2 | semidirect |
| 3. #14521346 | C2 | semidirect |
| 4. #14521336 | C2 | semidirect |
| 5. #14521326 | C2 | semidirect |
| 6. #14521089 | C2 | semidirect |
| 7. #14521085 | C2 | semidirect |
| 8. #14521076 | C2 | semidirect |
| 11. C31×#544 | C2 | semidirect |
| 14. C31×C4⋊Q8 | C22 | semidirect |
| 16. C31×#125 | C22 | semidirect |
| 33. #11758396 | C22 | semidirect |
| 34. #11758396 | C22 | semidirect |
| 35. #11758396 | C22 | semidirect |
| 36. #11758395 | C22 | semidirect |
| 37. #11758395 | C22 | semidirect |
| 38. #11758395 | C22 | semidirect |
| 39. C4⋊(C31⋊C8) | C22 | semidirect |
| 40. C4⋊(C31⋊C8) | C22 | semidirect |
| 47. C2×D124 | Q8 | semidirect |
| 120. #544 | D31 | semidirect |
| 140. C4⋊Q8 | C2×D31 | semidirect |
| 142. #125 | C2×D31 | semidirect |
| 165. C31 | #3081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521523 | 2 |
| #14521346 | 2 |
| #14521336 | 2 |
| #14521326 | 2 |
| #14521089 | 2 |
| #14521085 | 2 |
| #14521076 | 2 |
| #14521053 | 2 |
| C2×#11758397 | 2 |
| C31×#544 | 2 |
| #3081 | 31 |