Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
612 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 237 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×Q8×Dic31 | C2 | semidirect |
| 3. #14520956 | C2 | semidirect |
| 5. #14520942 | C2 | semidirect |
| 6. #14520924 | C2 | semidirect |
| 7. #14520919 | C2 | semidirect |
| 8. #14520895 | C2 | semidirect |
| 13. C31×#124 | C4 | semidirect |
| 33. C2×Q8×C31 | C2×C4 | semidirect |
| 47. C22⋊C4×C31 | C2×C4 | semidirect |
| 48. C42×C31 | C2×C4 | semidirect |
| 124. #124 | Dic31 | semidirect |
| 141. C31 | #2326 | semidirect |
| 145. C2×Q8 | C2×Dic31 | semidirect |
| 165. C22⋊C4 | C2×Dic31 | semidirect |
| 169. C42 | C2×Dic31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic31 | 2 |
| C2×D4×Dic31 | 2 |
| #14520956 | 2 |
| #14520952 | 2 |
| #14520942 | 2 |
| #14520924 | 2 |
| #14520919 | 2 |
| #14520895 | 2 |
| C2×C31×#124 | 2 |
| #2326 | 31 |