Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
512 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 309 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. #14521087 | C2 | direct (N × H) |
| 3. C2×#11758406 | C2 | semidirect |
| 4. C2×#11758405 | C2 | semidirect |
| 7. C22×C8×C31 | C4 | semidirect |
| 16. #11758406 | C22 | semidirect |
| 17. #11758405 | C22 | semidirect |
| 28. C2×C8×C31 | C2×C4 | semidirect |
| 70. C2×C31 | #427 | semidirect |
| 74. C22×C8 | Dic31 | semidirect |
| 85. C31 | C2×#427 | semidirect |
| 96. C2×C8 | C2×Dic31 | semidirect |
| 132. C2 | #14521087 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758503 | 2 |
| #14521087 | 2 |
| C2×#11758406 | 2 |
| C2×#11758405 | 2 |
| C23×C8×C31 | 2 |
| C2×#427 | 31 |