Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C4⋊C4×D157 | C2 | semidirect |
| 3. #23757590 | C2 | direct (N × H) |
| 4. C2×#19097703 | C2 | semidirect |
| 5. C2×#19097702 | C2 | semidirect |
| 6. C2×#19097692 | C2 | semidirect |
| 7. C2×#19097683 | C2 | semidirect |
| 8. C2×#102×C157 | C2 | semidirect |
| 19. C4⋊C4×D157 | C22 | semidirect |
| 21. #19097703 | C22 | semidirect |
| 22. #19097702 | C22 | semidirect |
| 23. #19097692 | C22 | semidirect |
| 24. #19097683 | C22 | semidirect |
| 28. #102×C157 | C22 | semidirect |
| 111. C2×C157 | #481 | semidirect |
| 116. C157 | C2×#481 | semidirect |
| 124. C2×#102 | D157 | semidirect |
| 144. #102 | C2×D157 | semidirect |
| 229. C2 | #23757590 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097742 | 2 |
| C2×C4⋊C4×D157 | 2 |
| #23757590 | 2 |
| C2×#19097703 | 2 |
| C2×#19097702 | 2 |
| C2×#19097692 | 2 |
| C2×#19097683 | 2 |
| C2×#102×C157 | 2 |
| C2×#481 | 157 |