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 |
|---|---|---|
| 1. #14521677 | C2 | semidirect |
| 3. #14521414 | C2 | semidirect |
| 4. #14521409 | C2 | semidirect |
| 5. #14521404 | C2 | semidirect |
| 6. #14521396 | C2 | semidirect |
| 7. #14521055 | C2 | semidirect |
| 8. #14521051 | C2 | semidirect |
| 9. #14521046 | C2 | semidirect |
| 10. C2×#11758409 | C2 | semidirect |
| 11. C31×#405 | C2 | semidirect |
| 27. #11758447 | C22 | semidirect |
| 28. #11758446 | C22 | semidirect |
| 29. C31×#97 | C22 | semidirect |
| 30. C4×C8×C31 | C22 | semidirect |
| 35. #11758409 | C22 | semidirect |
| 36. #11758409 | C22 | semidirect |
| 37. #11758409 | C22 | semidirect |
| 38. #11758404 | C22 | semidirect |
| 39. #11758404 | C22 | semidirect |
| 40. #11758404 | C22 | semidirect |
| 140. #405 | D31 | semidirect |
| 174. #97 | C2×D31 | semidirect |
| 175. C4×C8 | 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 |
|---|---|
| #14521677 | 2 |
| #14521618 | 2 |
| #14521414 | 2 |
| #14521409 | 2 |
| #14521404 | 2 |
| #14521396 | 2 |
| #14521055 | 2 |
| #14521051 | 2 |
| #14521046 | 2 |
| C2×#11758409 | 2 |
| C31×#405 | 2 |
| #3136 | 31 |