Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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×#11758388 | C2 | semidirect |
| 2. #14521290 | C2 | semidirect |
| 4. #14520877 | C2 | semidirect |
| 5. #14520854 | C2 | semidirect |
| 6. #14520851 | C2 | semidirect |
| 7. C22×C16×C31 | C2 | semidirect |
| 39. C16×C31 | D4 | semidirect |
| 60. C22×C31 | SD32 | semidirect |
| 72. C22×C16 | D31 | semidirect |
| 96. C31 | #2217 | semidirect |
| 115. C16 | C22⋊D31 | semidirect |
| 138. C22 | #11758388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758388 | 2 |
| #14521290 | 2 |
| #14521285 | 2 |
| #14520877 | 2 |
| #14520854 | 2 |
| #14520851 | 2 |
| C22×C16×C31 | 2 |
| #2217 | 31 |