Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#11758467 | C2 | semidirect |
| 3. #14521402 | C2 | direct (N × H) |
| 4. C2×#11758404 | C2 | semidirect |
| 5. C2×#11758398 | C2 | semidirect |
| 7. C2×C8×Dic31 | C2 | semidirect |
| 23. #11758467 | C22 | semidirect |
| 26. #11758404 | C22 | semidirect |
| 27. C8×Dic31 | C22 | semidirect |
| 28. #11758398 | C22 | semidirect |
| 111. C2×C31 | #488 | semidirect |
| 135. C31 | C2×#488 | semidirect |
| 209. C2 | #14521402 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758467 | 2 |
| C2×#11758513 | 2 |
| #14521402 | 2 |
| C2×#11758404 | 2 |
| C2×#11758398 | 2 |
| C2×#11758420 | 2 |
| C2×C8×Dic31 | 2 |
| C2×C31×#102 | 2 |
| C2×#488 | 31 |