Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
488 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 213 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. #14521105 | C2 | direct (N × H) |
| 3. C2×C4⋊(C31⋊C8) | C2 | semidirect |
| 5. C2×#11758403 | C2 | semidirect |
| 6. C2×C31×C4⋊C8 | C2 | semidirect |
| 18. C31×C4⋊C8 | C22 | semidirect |
| 20. #11758403 | C22 | semidirect |
| 21. C4⋊(C31⋊C8) | C22 | semidirect |
| 93. C2×C4⋊C8 | D31 | semidirect |
| 96. C2×C31 | #432 | semidirect |
| 113. C4⋊C8 | C2×D31 | semidirect |
| 116. C31 | C2×#432 | semidirect |
| 185. C2 | #14521105 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D31 | 2 |
| #14521105 | 2 |
| C2×C4⋊(C31⋊C8) | 2 |
| C2×(C2×D31)⋊C8 | 2 |
| C2×#11758403 | 2 |
| C2×C31×C4⋊C8 | 2 |
| C2×#432 | 31 |