Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23757904 | C2 | semidirect |
| 3. #23757576 | C2 | semidirect |
| 4. #23757572 | C2 | semidirect |
| 5. #23757562 | C2 | semidirect |
| 6. #23757552 | C2 | semidirect |
| 7. #23757309 | C2 | semidirect |
| 8. #23757301 | C2 | semidirect |
| 11. #428×C157 | C2 | semidirect |
| 15. #19097770 | C22 | semidirect |
| 17. #19097762 | C22 | semidirect |
| 26. #19097704 | C22 | semidirect |
| 27. #19097704 | C22 | semidirect |
| 28. #19097702 | C22 | semidirect |
| 29. #19097702 | C22 | semidirect |
| 30. #19097700 | C22 | semidirect |
| 31. #19097700 | C22 | semidirect |
| 39. #107×C157 | C22 | semidirect |
| 40. #106×C157 | C22 | semidirect |
| 45. C2×D628 | Q8 | semidirect |
| 124. C157 | #3081 | semidirect |
| 132. #428 | D157 | semidirect |
| 156. #107 | C2×D157 | semidirect |
| 159. #106 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757904 | 2 |
| #23757747 | 2 |
| #23757576 | 2 |
| #23757572 | 2 |
| #23757562 | 2 |
| #23757552 | 2 |
| #23757309 | 2 |
| #23757301 | 2 |
| #23757279 | 2 |
| C2×#19097691 | 2 |
| #428×C157 | 2 |
| #3081 | 157 |