Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14521415 | C2 | semidirect |
| 3. #14521411 | C2 | semidirect |
| 4. #14521406 | C2 | semidirect |
| 5. #14521397 | C2 | semidirect |
| 6. #14521053 | C2 | semidirect |
| 7. #14521048 | C2 | semidirect |
| 8. #14521043 | C2 | semidirect |
| 9. C2×#11758397 | C2 | semidirect |
| 10. #14521005 | C2 | semidirect |
| 11. C31×#544 | C2 | semidirect |
| 15. C31×C4⋊Q8 | C22 | semidirect |
| 17. C31×#125 | C22 | semidirect |
| 29. #11758398 | C22 | semidirect |
| 30. #11758398 | C22 | semidirect |
| 31. #11758398 | C22 | semidirect |
| 36. #11758397 | C22 | semidirect |
| 37. #11758397 | C22 | semidirect |
| 38. #11758397 | C22 | semidirect |
| 39. #11758391 | C22 | semidirect |
| 40. C4×C31⋊C8 | C22 | semidirect |
| 130. #544 | D31 | semidirect |
| 152. C4⋊Q8 | C2×D31 | semidirect |
| 155. #125 | C2×D31 | semidirect |
| 176. C31 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521618 | 2 |
| #14521415 | 2 |
| #14521411 | 2 |
| #14521406 | 2 |
| #14521397 | 2 |
| #14521053 | 2 |
| #14521048 | 2 |
| #14521043 | 2 |
| C2×#11758397 | 2 |
| #14521005 | 2 |
| C31×#544 | 2 |
| #3136 | 31 |