Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #14521090 | C2 | semidirect |
| 4. #14521088 | C2 | semidirect |
| 5. #14521087 | C2 | semidirect |
| 6. #14521085 | C2 | semidirect |
| 7. C31×#427 | C2 | semidirect |
| 13. C2×#92469 | C4 | semidirect |
| 22. C31×#107 | C22 | semidirect |
| 23. C31×#106 | C22 | semidirect |
| 24. #11758406 | C22 | semidirect |
| 25. #11758405 | C22 | semidirect |
| 26. #11758396 | C22 | semidirect |
| 27. #11758395 | C22 | semidirect |
| 36. C2×C8×C31 | C2×C4 | semidirect |
| 48. C2×C31⋊C8 | C2×C4 | semidirect |
| 50. #92469 | C2×C4 | semidirect |
| 51. #92469 | C2×C4 | semidirect |
| 90. #427 | D31 | semidirect |
| 111. #107 | C2×D31 | semidirect |
| 114. #106 | C2×D31 | semidirect |
| 115. C31 | #2911 | semidirect |
| 128. C2×C8 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92469 | 2 |
| #117×D31 | 2 |
| #14521090 | 2 |
| #14521088 | 2 |
| #14521087 | 2 |
| #14521085 | 2 |
| C31×#427 | 2 |
| #2911 | 31 |