Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C2×#19097801 | C2 | semidirect |
| 3. C2×#19097759 | C2 | semidirect |
| 4. #23757495 | C2 | semidirect |
| 5. #23757488 | C2 | semidirect |
| 6. #23757297 | C2 | semidirect |
| 7. #23757281 | C2 | semidirect |
| 8. #23757277 | C2 | semidirect |
| 9. C4×#41×C157 | C2 | semidirect |
| 14. C2×#14578944 | C22 | semidirect |
| 15. C2×#14578942 | C22 | semidirect |
| 24. C4⋊#11929434 | C22 | semidirect |
| 25. #19097694 | C22 | semidirect |
| 28. C4×Q8×C157 | C22 | semidirect |
| 30. C4×D4×C157 | C22 | semidirect |
| 125. C157 | #3040 | semidirect |
| 130. C4×#41 | D157 | semidirect |
| 150. C4×Q8 | C2×D157 | semidirect |
| 152. C4×D4 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097801 | 2 |
| C2×#19097796 | 2 |
| C2×#19097759 | 2 |
| #23757495 | 2 |
| #23757488 | 2 |
| #23757297 | 2 |
| #23757281 | 2 |
| #23757277 | 2 |
| C4×#41×C157 | 2 |
| #3040 | 157 |