Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C2×#11758527 | C2 | semidirect |
| 2. #14521599 | C2 | semidirect |
| 3. #14521444 | C2 | semidirect |
| 4. #14521441 | C2 | semidirect |
| 5. #14521439 | C2 | semidirect |
| 6. #14521436 | C2 | semidirect |
| 7. C2×#11758391 | C2 | semidirect |
| 8. C31×#532 | C2 | semidirect |
| 55. C2×C31⋊C8 | D4 | semidirect |
| 95. #532 | D31 | semidirect |
| 127. C31 | #3150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758527 | 2 |
| #14521599 | 2 |
| #14521444 | 2 |
| #14521441 | 2 |
| #14521439 | 2 |
| #14521436 | 2 |
| C2×#11758391 | 2 |
| C31×#532 | 2 |
| #3150 | 31 |