Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#92470 | C2 | semidirect |
| 2. C22×#92480 | C2 | semidirect |
| 4. C2×#11758464 | C2 | semidirect |
| 5. #14521248 | C2 | direct (N × H) |
| 6. C2×Dic31⋊C8 | C2 | semidirect |
| 7. C2×#11758397 | C2 | semidirect |
| 8. C2×C31×#102 | C2 | semidirect |
| 19. C2×#92480 | C22 | semidirect |
| 25. C2×#92470 | C22 | semidirect |
| 27. #11758464 | C22 | semidirect |
| 28. C31×#102 | C22 | semidirect |
| 29. Dic31⋊C8 | C22 | semidirect |
| 30. #11758397 | C22 | semidirect |
| 52. C2×Dic62 | D4 | semidirect |
| 89. C2×Dic31 | SD16 | semidirect |
| 97. Dic62 | C2×D4 | semidirect |
| 119. Dic31 | C2×SD16 | semidirect |
| 127. C2×#102 | D31 | semidirect |
| 129. C2×C31 | #460 | semidirect |
| 155. #102 | C2×D31 | semidirect |
| 156. C31 | C2×#460 | semidirect |
| 247. C2 | #14521248 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92470 | 2 |
| C22×#92480 | 2 |
| C2×#11758517 | 2 |
| C2×#11758464 | 2 |
| #14521248 | 2 |
| C2×Dic31⋊C8 | 2 |
| C2×#11758397 | 2 |
| C2×C31×#102 | 2 |
| C2×#460 | 31 |