Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
740 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#92482 | C2 | semidirect |
| 4. #14521203 | C2 | direct (N × H) |
| 5. C2×#11758404 | C2 | semidirect |
| 6. C2×#11758423 | C2 | semidirect |
| 8. C22×Q16×C31 | C2 | semidirect |
| 20. C2×Q16×C31 | C22 | semidirect |
| 25. C2×#92482 | C22 | semidirect |
| 30. #11758423 | C22 | semidirect |
| 32. #11758404 | C22 | semidirect |
| 76. C22×D31 | Q16 | semidirect |
| 116. C2×D31 | C2×Q16 | semidirect |
| 127. C22×Q16 | D31 | semidirect |
| 133. C2×C31 | #451 | semidirect |
| 151. C2×Q16 | C2×D31 | semidirect |
| 162. C31 | C2×#451 | semidirect |
| 255. C2 | #14521203 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D31 | 2 |
| C22×#92482 | 2 |
| C2×#11758523 | 2 |
| #14521203 | 2 |
| C2×#11758404 | 2 |
| C2×#11758423 | 2 |
| C2×(C2×D31)⋊C8 | 2 |
| C22×Q16×C31 | 2 |
| C2×#451 | 31 |