Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1008 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×#92469 | C2 | semidirect |
| 3. C2×#11758469 | C2 | semidirect |
| 4. #14521052 | C2 | direct (N × H) |
| 5. C2×#11758409 | C2 | semidirect |
| 6. C2×#11758420 | C2 | semidirect |
| 7. C2×#11758397 | C2 | semidirect |
| 8. C2×C31×#102 | C2 | semidirect |
| 14. C2×D4×D31 | C4 | semidirect |
| 18. C22×C8×C31 | C22 | semidirect |
| 19. C2×C4⋊C4×C31 | C22 | semidirect |
| 21. C2×C4⋊Dic31 | C22 | semidirect |
| 23. C22×C31⋊C8 | C22 | semidirect |
| 25. C2×#92469 | C22 | semidirect |
| 27. #11758469 | C22 | semidirect |
| 28. C31×#102 | C22 | semidirect |
| 29. #11758420 | C22 | semidirect |
| 30. #11758409 | C22 | semidirect |
| 31. #11758397 | C22 | semidirect |
| 51. D4×D31 | C2×C4 | semidirect |
| 61. C2×C8×C31 | C23 | semidirect |
| 63. C4⋊C4×C31 | C23 | semidirect |
| 66. C4⋊Dic31 | C23 | semidirect |
| 69. C2×C31⋊C8 | C23 | semidirect |
| 141. C2×#102 | D31 | semidirect |
| 143. C2×C31 | #418 | semidirect |
| 161. C22×C8 | C2×D31 | semidirect |
| 165. C2×C4⋊C4 | C2×D31 | semidirect |
| 171. #102 | C2×D31 | semidirect |
| 172. C31 | C2×#418 | semidirect |
| 205. C2×C8 | C22×D31 | semidirect |
| 209. C4⋊C4 | C22×D31 | semidirect |
| 277. C2 | #14521052 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D31 | 2 |
| C22×#92469 | 2 |
| C2×#11758469 | 2 |
| #14521052 | 2 |
| C2×#11758409 | 2 |
| C2×#11758420 | 2 |
| C2×#11758397 | 2 |
| C2×C31×#102 | 2 |
| C2×#418 | 31 |