Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11758509 | C2 | semidirect |
| 2. C2×#11758481 | C2 | semidirect |
| 3. #14521616 | C2 | semidirect |
| 4. #14521437 | C2 | semidirect |
| 5. #14521432 | C2 | semidirect |
| 6. #14521424 | C2 | semidirect |
| 7. #14521004 | C2 | semidirect |
| 8. C22×D8×C31 | C2 | semidirect |
| 16. #11758517 | C22 | semidirect |
| 18. #11758513 | C22 | semidirect |
| 19. C2×#92480 | C22 | semidirect |
| 21. C2×#92479 | C22 | semidirect |
| 24. C2×Dic124 | C22 | semidirect |
| 26. C2×D248 | C22 | semidirect |
| 27. C2×#92470 | C22 | semidirect |
| 28. #11758403 | C22 | semidirect |
| 29. C8×Dic31 | C22 | semidirect |
| 45. C2×C8×C31 | D4 | semidirect |
| 54. #92474 | D4 | semidirect |
| 99. C22×D8 | D31 | semidirect |
| 131. C31 | #3155 | semidirect |
| 154. C2×C8 | C22⋊D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758509 | 2 |
| C2×#11758481 | 2 |
| #14521616 | 2 |
| #14521437 | 2 |
| #14521432 | 2 |
| #14521424 | 2 |
| #14521004 | 2 |
| C22×D8×C31 | 2 |
| #3155 | 31 |