Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
528 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 145 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. C4⋊Q8×D157 | C2 | semidirect |
| 3. #23757621 | C2 | semidirect |
| 4. #23757620 | C2 | semidirect |
| 5. #23757619 | C2 | semidirect |
| 6. #23757618 | C2 | semidirect |
| 7. #102×D157 | C2 | semidirect |
| 8. C4×C8×D157 | C2 | semidirect |
| 9. #486×C157 | C2 | semidirect |
| 15. #19097771 | C22 | semidirect |
| 17. #19097770 | C22 | semidirect |
| 26. #19097693 | C22 | semidirect |
| 27. #19097692 | C22 | semidirect |
| 28. #19097691 | C22 | semidirect |
| 29. C4×#11929434 | C22 | semidirect |
| 30. C8×Dic157 | C22 | semidirect |
| 31. C4⋊Q8×C157 | C22 | semidirect |
| 33. #102×C157 | C22 | semidirect |
| 34. C4×C8×C157 | C22 | semidirect |
| 125. D157 | #486 | direct (N × H) |
| 126. C157 | C2×#486 | semidirect |
| 134. #486 | D157 | direct (N × H) |
| 146. C4⋊Q8 | C2×D157 | semidirect |
| 158. #102 | C2×D157 | semidirect |
| 161. C4×C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D157 | 2 |
| #127×D157 | 2 |
| #23757621 | 2 |
| #23757620 | 2 |
| #23757619 | 2 |
| #23757618 | 2 |
| #102×D157 | 2 |
| C4×C8×D157 | 2 |
| #486×C157 | 2 |
| C2×#486 | 157 |