Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23757570 | C2 | semidirect |
| 3. #23757570 | C2 | semidirect |
| 4. #23757560 | C2 | semidirect |
| 5. #23757550 | C2 | semidirect |
| 6. #23757313 | C2 | semidirect |
| 7. #23757309 | C2 | semidirect |
| 8. #23757300 | C2 | semidirect |
| 11. #544×C157 | C2 | semidirect |
| 21. #19097704 | C22 | semidirect |
| 22. #19097704 | C22 | semidirect |
| 23. #19097704 | C22 | semidirect |
| 24. #19097702 | C22 | semidirect |
| 25. #19097702 | C22 | semidirect |
| 26. #19097702 | C22 | semidirect |
| 27. C4⋊#11929434 | C22 | semidirect |
| 28. C4⋊#11929434 | C22 | semidirect |
| 34. C4⋊Q8×C157 | C22 | semidirect |
| 36. #125×C157 | C22 | semidirect |
| 44. C2×D628 | Q8 | semidirect |
| 124. C157 | #3081 | semidirect |
| 126. #544 | D157 | semidirect |
| 141. C4⋊Q8 | C2×D157 | semidirect |
| 143. #125 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757747 | 2 |
| #23757570 | 2 |
| #23757560 | 2 |
| #23757550 | 2 |
| #23757313 | 2 |
| #23757309 | 2 |
| #23757300 | 2 |
| #23757277 | 2 |
| C2×#19097691 | 2 |
| #544×C157 | 2 |
| #3081 | 157 |