Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23757984 | C2 | semidirect |
| 3. #23757590 | C2 | semidirect |
| 4. #23757560 | C2 | semidirect |
| 5. #23757501 | C2 | semidirect |
| 6. #23757470 | C2 | semidirect |
| 7. #23757425 | C2 | semidirect |
| 8. C4×#14578943 | C2 | semidirect |
| 9. C8×D628 | C2 | semidirect |
| 10. #102×D157 | C2 | semidirect |
| 11. #486×C157 | C2 | semidirect |
| 15. C2×#14578942 | C22 | semidirect |
| 16. C2×C8×D157 | C22 | semidirect |
| 18. #19097751 | C22 | semidirect |
| 23. C4×Dic314 | C22 | semidirect |
| 27. C4⋊C4×D157 | C22 | semidirect |
| 28. #19097703 | C22 | semidirect |
| 29. #19097702 | C22 | semidirect |
| 30. C4⋊#11929434 | C22 | semidirect |
| 31. #19097696 | C22 | semidirect |
| 33. #19097692 | C22 | semidirect |
| 35. #19097683 | C22 | semidirect |
| 36. C4⋊Q8×C157 | C22 | semidirect |
| 38. #102×C157 | C22 | semidirect |
| 39. #102×C157 | C22 | semidirect |
| 40. C4×C8×C157 | C22 | semidirect |
| 85. D628 | SD16 | semidirect |
| 136. C157 | #3295 | semidirect |
| 140. #486 | D157 | semidirect |
| 154. C4⋊Q8 | C2×D157 | semidirect |
| 174. #102 | C2×D157 | semidirect |
| 175. #102 | C2×D157 | semidirect |
| 177. C4×C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757984 | 2 |
| #23757908 | 2 |
| #23757590 | 2 |
| #23757560 | 2 |
| #23757501 | 2 |
| #23757470 | 2 |
| #23757425 | 2 |
| C4×#14578943 | 2 |
| C8×D628 | 2 |
| #102×D157 | 2 |
| #486×C157 | 2 |
| #3295 | 157 |