Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23757885 | C2 | semidirect |
| 3. #23757615 | C2 | semidirect |
| 4. #23757574 | C2 | semidirect |
| 5. #23757479 | C2 | semidirect |
| 7. #23757375 | C2 | semidirect |
| 8. C4×#14578943 | C2 | semidirect |
| 9. #433×C157 | C2 | semidirect |
| 13. #19097771 | C22 | semidirect |
| 15. #19097763 | C22 | semidirect |
| 18. C4×Dic314 | C22 | semidirect |
| 24. #19097705 | C22 | semidirect |
| 25. #19097703 | C22 | semidirect |
| 26. #19097696 | C22 | semidirect |
| 27. #19097696 | C22 | semidirect |
| 31. C4⋊C8×C157 | C22 | semidirect |
| 33. #97×C157 | C22 | semidirect |
| 34. C4×C8×C157 | C22 | semidirect |
| 102. C157 | #3123 | semidirect |
| 112. #433 | D157 | semidirect |
| 130. C4⋊C8 | C2×D157 | semidirect |
| 136. #97 | C2×D157 | semidirect |
| 137. C4×C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757885 | 2 |
| #23757747 | 2 |
| #23757615 | 2 |
| #23757574 | 2 |
| #23757479 | 2 |
| #23757426 | 2 |
| #23757375 | 2 |
| C4×#14578943 | 2 |
| #433×C157 | 2 |
| #3123 | 157 |