Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 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. C2×Q8×Dic31 | C2 | semidirect |
| 5. #14520941 | C2 | semidirect |
| 6. #14520914 | C2 | semidirect |
| 7. #14520896 | C2 | semidirect |
| 8. C42×Dic31 | C2 | semidirect |
| 9. C31×#391 | C2 | semidirect |
| 15. #11758524 | C4 | semidirect |
| 33. C2×Q8×C31 | C2×C4 | semidirect |
| 51. (C2×D31)⋊C4 | C2×C4 | semidirect |
| 57. C4×Dic31 | C2×C4 | semidirect |
| 106. Dic31 | #124 | semidirect |
| 110. #391 | D31 | semidirect |
| 142. C31 | C4×#124 | semidirect |
| 146. C2×Q8 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758524 | 2 |
| C2×Q8×Dic31 | 2 |
| C2×#11758470 | 2 |
| #14520951 | 2 |
| #14520941 | 2 |
| #14520914 | 2 |
| #14520896 | 2 |
| C42×Dic31 | 2 |
| C31×#391 | 2 |
| C4×#124 | 31 |