Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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. #14521406 | C2 | direct (N × H) |
| 3. C2×#11758398 | C2 | semidirect |
| 5. C2×C4×C31⋊C8 | C2 | semidirect |
| 6. C2×C31×#125 | C2 | semidirect |
| 10. C31×#125 | C22 | semidirect |
| 18. #11758398 | C22 | semidirect |
| 20. C4×C31⋊C8 | C22 | semidirect |
| 70. C2×#125 | D31 | semidirect |
| 76. C2×C31 | #488 | semidirect |
| 84. #125 | C2×D31 | semidirect |
| 94. C31 | C2×#488 | semidirect |
| 144. C2 | #14521406 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758452 | 2 |
| #14521406 | 2 |
| C2×#11758398 | 2 |
| C2×#11758397 | 2 |
| C2×C4×C31⋊C8 | 2 |
| C2×C31×#125 | 2 |
| C2×#488 | 31 |