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 |
|---|---|---|
| 1. #23757901 | C2 | semidirect |
| 3. #23757575 | C2 | semidirect |
| 4. #23757571 | C2 | semidirect |
| 5. #23757561 | C2 | semidirect |
| 6. #23757551 | C2 | semidirect |
| 7. #23757315 | C2 | semidirect |
| 8. #23757309 | C2 | semidirect |
| 9. #23757301 | C2 | semidirect |
| 14. #19097770 | C22 | semidirect |
| 16. #19097762 | C22 | semidirect |
| 26. #19097705 | C22 | semidirect |
| 27. #19097704 | C22 | semidirect |
| 28. #19097704 | C22 | semidirect |
| 29. #19097703 | C22 | semidirect |
| 30. #19097702 | C22 | semidirect |
| 31. #19097702 | C22 | semidirect |
| 32. #19097700 | C22 | semidirect |
| 33. #19097700 | C22 | semidirect |
| 66. C2×D4×C157 | Q8 | semidirect |
| 124. C157 | #3081 | semidirect |
| 170. C2×D4 | Dic314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757901 | 2 |
| #23757748 | 2 |
| #23757575 | 2 |
| #23757571 | 2 |
| #23757561 | 2 |
| #23757551 | 2 |
| #23757315 | 2 |
| #23757309 | 2 |
| #23757301 | 2 |
| C2×#19097692 | 2 |
| #418×C157 | 2 |
| #3081 | 157 |