Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #14521527 | C2 | semidirect |
| 4. #14521152 | C2 | semidirect |
| 5. #14521134 | C2 | semidirect |
| 6. #14521085 | C2 | semidirect |
| 8. #14521007 | C2 | semidirect |
| 9. C31×#419 | C2 | semidirect |
| 15. Q8×Dic31 | C22 | semidirect |
| 16. C2×#92481 | C4 | semidirect |
| 26. C31×#103 | C22 | semidirect |
| 28. #11758403 | C22 | semidirect |
| 29. C8×Dic31 | C22 | semidirect |
| 30. #11758396 | C22 | semidirect |
| 31. #11758395 | C22 | semidirect |
| 35. C2×Q8×C31 | C2×C4 | semidirect |
| 51. #92481 | C2×C4 | semidirect |
| 52. #92481 | C2×C4 | semidirect |
| 60. C2×C31⋊C8 | C2×C4 | semidirect |
| 106. #419 | D31 | semidirect |
| 131. #103 | C2×D31 | semidirect |
| 135. C31 | #2949 | semidirect |
| 139. C2×Q8 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92481 | 2 |
| #14521527 | 2 |
| #14521523 | 2 |
| #14521152 | 2 |
| #14521134 | 2 |
| #14521085 | 2 |
| #14521055 | 2 |
| #14521007 | 2 |
| C31×#419 | 2 |
| #2949 | 31 |