Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11758521 | C2 | semidirect |
| 4. #14521252 | C2 | direct (N × H) |
| 5. C2×Dic31⋊C8 | C2 | semidirect |
| 6. C2×#11758404 | C2 | semidirect |
| 7. C2×#11758423 | C2 | semidirect |
| 18. #11758521 | C22 | semidirect |
| 28. #11758423 | C22 | semidirect |
| 29. #11758404 | C22 | semidirect |
| 30. Dic31⋊C8 | C22 | semidirect |
| 88. C2×Dic31 | SD16 | semidirect |
| 112. Dic31 | C2×SD16 | semidirect |
| 122. C2×C31 | #461 | semidirect |
| 148. C31 | C2×#461 | semidirect |
| 231. C2 | #14521252 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92480 | 2 |
| C2×#11758521 | 2 |
| C2×D4×Dic31 | 2 |
| #14521252 | 2 |
| C2×Dic31⋊C8 | 2 |
| C2×#11758404 | 2 |
| C2×#11758423 | 2 |
| C22×SD16×C31 | 2 |
| C2×#461 | 31 |