Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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. D4×Dic62 | C2 | semidirect |
| 2. #14521396 | C2 | semidirect |
| 3. #14521250 | C2 | semidirect |
| 5. #14520796 | C2 | semidirect |
| 6. #14520781 | C2 | semidirect |
| 7. C31×D4⋊C8 | C2 | semidirect |
| 54. D4×C31 | SD16 | semidirect |
| 74. Dic62 | D8 | semidirect |
| 101. D4⋊C8 | D31 | semidirect |
| 124. C31 | #1627 | semidirect |
| 164. D4 | #92470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic62 | 2 |
| #14521396 | 2 |
| #14521250 | 2 |
| #14521244 | 2 |
| #14520796 | 2 |
| #14520781 | 2 |
| C31×D4⋊C8 | 2 |
| #1627 | 31 |