Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#92470 | C2 | semidirect |
| 2. C22×C8×D31 | C2 | semidirect |
| 3. C2×#11758474 | C2 | semidirect |
| 5. #14521279 | C2 | direct (N × H) |
| 6. C2×#11758398 | C2 | semidirect |
| 7. C2×#11758397 | C2 | semidirect |
| 8. C2×C31×#106 | C2 | semidirect |
| 21. C2×#92470 | C22 | semidirect |
| 23. C2×C8×D31 | C22 | semidirect |
| 25. #11758474 | C22 | semidirect |
| 28. C31×#106 | C22 | semidirect |
| 29. #11758398 | C22 | semidirect |
| 30. #11758397 | C22 | semidirect |
| 52. C2×C8×C31 | D4 | semidirect |
| 72. C22×D31 | SD16 | semidirect |
| 96. C8×C31 | C2×D4 | semidirect |
| 110. C2×D31 | C2×SD16 | semidirect |
| 123. C2×#106 | D31 | semidirect |
| 126. C2×C31 | #465 | semidirect |
| 151. #106 | C2×D31 | semidirect |
| 154. C31 | C2×#465 | semidirect |
| 180. C2×C8 | D124 | semidirect |
| 221. C8 | C2×D124 | semidirect |
| 243. C2 | #14521279 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92470 | 2 |
| C22×C8×D31 | 2 |
| C2×#11758474 | 2 |
| C2×#11758472 | 2 |
| #14521279 | 2 |
| C2×#11758398 | 2 |
| C2×#11758397 | 2 |
| C2×C31×#106 | 2 |
| C2×#465 | 31 |