Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C22×#92480 | C2 | semidirect |
| 3. C2×#11758452 | C2 | semidirect |
| 4. #14521264 | C2 | direct (N × H) |
| 5. C2×C4⋊(C31⋊C8) | C2 | semidirect |
| 6. C2×#11758398 | C2 | semidirect |
| 7. C2×#11758397 | C2 | semidirect |
| 8. C2×C4×D4×C31 | C2 | semidirect |
| 14. C4×D4×C31 | C22 | semidirect |
| 19. C2×#92480 | C22 | semidirect |
| 27. #11758452 | C22 | semidirect |
| 28. #11758398 | C22 | semidirect |
| 29. #11758397 | C22 | semidirect |
| 30. C4⋊(C31⋊C8) | C22 | semidirect |
| 121. C2×C4×D4 | D31 | semidirect |
| 127. C2×C31 | #463 | semidirect |
| 145. C4×D4 | C2×D31 | semidirect |
| 154. C31 | C2×#463 | semidirect |
| 243. C2 | #14521264 | 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 |
| C22×#92479 | 2 |
| C2×#11758452 | 2 |
| #14521264 | 2 |
| C2×C4⋊(C31⋊C8) | 2 |
| C2×#11758398 | 2 |
| C2×#11758397 | 2 |
| C2×C4×D4×C31 | 2 |
| C2×#463 | 31 |