Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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×#11758496 | C2 | semidirect |
| 2. #14521718 | C2 | semidirect |
| 3. #14521424 | C2 | semidirect |
| 4. #14521285 | C2 | semidirect |
| 5. #14521282 | C2 | semidirect |
| 6. #14521247 | C2 | semidirect |
| 7. #14521194 | C2 | semidirect |
| 8. #14521193 | C2 | semidirect |
| 9. Q16×Dic31 | C2 | semidirect |
| 10. C8×C22⋊D31 | C2 | semidirect |
| 11. C2×C31×#135 | C2 | semidirect |
| 59. Q16×C31 | D4 | semidirect |
| 135. Dic31 | #135 | semidirect |
| 137. C2×#135 | D31 | semidirect |
| 183. C31 | #3287 | semidirect |
| 202. Q16 | C22⋊D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758496 | 2 |
| #14521718 | 2 |
| #14521424 | 2 |
| #14521285 | 2 |
| #14521282 | 2 |
| #14521247 | 2 |
| #14521194 | 2 |
| #14521193 | 2 |
| Q16×Dic31 | 2 |
| C8×C22⋊D31 | 2 |
| C2×C31×#135 | 2 |
| #3287 | 31 |