Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
540 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 217 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. #14520956 | C2 | semidirect |
| 2. #14520942 | C2 | semidirect |
| 3. #14520942 | C2 | semidirect |
| 5. #14520924 | C2 | semidirect |
| 6. #14520917 | C2 | semidirect |
| 7. C4×C4⋊Dic31 | C2 | semidirect |
| 8. C22⋊C4×Dic31 | C2 | semidirect |
| 13. C31×#124 | C4 | semidirect |
| 34. C2×Q8×C31 | C2×C4 | semidirect |
| 48. C22⋊C4×C31 | C2×C4 | semidirect |
| 49. C22⋊C4×C31 | C2×C4 | semidirect |
| 50. C42×C31 | C2×C4 | semidirect |
| 131. #124 | Dic31 | semidirect |
| 150. C31 | #2337 | semidirect |
| 153. C2×Q8 | C2×Dic31 | semidirect |
| 172. C22⋊C4 | C2×Dic31 | semidirect |
| 173. C22⋊C4 | C2×Dic31 | semidirect |
| 177. C42 | C2×Dic31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14520956 | 2 |
| #14520942 | 2 |
| #14520929 | 2 |
| #14520924 | 2 |
| #14520917 | 2 |
| C4×C4⋊Dic31 | 2 |
| C22⋊C4×Dic31 | 2 |
| C2×C31×#124 | 2 |
| #2337 | 31 |