Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
444 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14521601 | C2 | semidirect |
| 3. #14521385 | C2 | semidirect |
| 4. #14521382 | C2 | semidirect |
| 5. #14521327 | C2 | semidirect |
| 6. #14521252 | C2 | semidirect |
| 8. #14521150 | C2 | semidirect |
| 9. #14521146 | C2 | semidirect |
| 10. #14521103 | C2 | semidirect |
| 17. Q8×Dic31 | C22 | semidirect |
| 18. #11758521 | C22 | semidirect |
| 28. #11758465 | C22 | semidirect |
| 30. #11758464 | C22 | semidirect |
| 35. #11758423 | C22 | semidirect |
| 38. #11758406 | C22 | semidirect |
| 39. #11758404 | C22 | semidirect |
| 40. #11758403 | C22 | semidirect |
| 41. Dic31⋊C8 | C22 | semidirect |
| 42. #11758395 | C22 | semidirect |
| 179. C31 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521601 | 2 |
| C2×D4×Dic31 | 2 |
| #14521385 | 2 |
| #14521382 | 2 |
| #14521327 | 2 |
| #14521252 | 2 |
| #14521200 | 2 |
| #14521150 | 2 |
| #14521146 | 2 |
| #14521103 | 2 |
| C31×#450 | 2 |
| #3110 | 31 |