Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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. #14521560 | C2 | semidirect |
| 3. #14521290 | C2 | semidirect |
| 4. #14521285 | C2 | semidirect |
| 5. #14521278 | C2 | semidirect |
| 6. #14521087 | C2 | semidirect |
| 7. #14521046 | C2 | semidirect |
| 8. C23×C8×C31 | C2 | semidirect |
| 22. C2×Dic124 | C22 | semidirect |
| 24. C2×D248 | C22 | semidirect |
| 25. C2×#92470 | C22 | semidirect |
| 26. #11758409 | C22 | semidirect |
| 27. #11758406 | C22 | semidirect |
| 28. #11758405 | C22 | semidirect |
| 29. #11758404 | C22 | semidirect |
| 47. C2×C8×C31 | D4 | semidirect |
| 92. C22×C31 | #135 | semidirect |
| 103. C23×C8 | D31 | semidirect |
| 136. C31 | #3050 | semidirect |
| 157. C2×C8 | C22⋊D31 | semidirect |
| 199. C22 | #11758481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758481 | 2 |
| #14521560 | 2 |
| #14521290 | 2 |
| #14521285 | 2 |
| #14521278 | 2 |
| #14521087 | 2 |
| #14521046 | 2 |
| C23×C8×C31 | 2 |
| #3050 | 31 |