Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 2. C2×#11758467 | C2 | semidirect |
| 3. #14521412 | C2 | direct (N × H) |
| 4. C2×#11758409 | C2 | semidirect |
| 5. C2×#11758420 | C2 | semidirect |
| 6. C2×#11758397 | C2 | semidirect |
| 7. C2×#11758403 | C2 | semidirect |
| 8. C2×C31×#102 | C2 | semidirect |
| 23. #11758467 | C22 | semidirect |
| 24. C31×#102 | C22 | semidirect |
| 25. #11758420 | C22 | semidirect |
| 26. #11758409 | C22 | semidirect |
| 27. #11758403 | C22 | semidirect |
| 28. #11758397 | C22 | semidirect |
| 117. C2×#102 | D31 | semidirect |
| 120. C2×C31 | #490 | semidirect |
| 143. #102 | C2×D31 | semidirect |
| 145. C31 | C2×#490 | semidirect |
| 229. C2 | #14521412 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758517 | 2 |
| C2×#11758467 | 2 |
| #14521412 | 2 |
| C2×#11758409 | 2 |
| C2×#11758420 | 2 |
| C2×#11758397 | 2 |
| C2×#11758403 | 2 |
| C2×C31×#102 | 2 |
| C2×#490 | 31 |