Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11758481 | C2 | semidirect |
| 2. #14521479 | C2 | direct (N × H) |
| 3. C2×#11758417 | C2 | semidirect |
| 4. C2×#11758415 | C2 | semidirect |
| 5. C2×#11758416 | C2 | semidirect |
| 6. C2×#11758414 | C2 | semidirect |
| 7. C22×C31⋊C16 | C2 | semidirect |
| 8. C2×C31×#135 | C2 | semidirect |
| 12. C31×#135 | C22 | semidirect |
| 19. #11758481 | C22 | semidirect |
| 22. #11758417 | C22 | semidirect |
| 23. #11758416 | C22 | semidirect |
| 24. #11758415 | C22 | semidirect |
| 25. #11758414 | C22 | semidirect |
| 28. C2×C31⋊C16 | C22 | semidirect |
| 96. C2×#135 | D31 | semidirect |
| 105. C2×C31 | #508 | semidirect |
| 113. #135 | C2×D31 | semidirect |
| 128. C31 | C2×#508 | semidirect |
| 197. C2 | #14521479 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758481 | 2 |
| #14521479 | 2 |
| C2×#11758417 | 2 |
| C2×#11758415 | 2 |
| C2×#11758416 | 2 |
| C2×#11758414 | 2 |
| C22×C31⋊C16 | 2 |
| C2×C31×#135 | 2 |
| C2×#508 | 31 |