Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #23757901 | C2 | semidirect |
| 3. #23757638 | C2 | semidirect |
| 4. #23757633 | C2 | semidirect |
| 5. #23757628 | C2 | semidirect |
| 6. #23757620 | C2 | semidirect |
| 7. #23757279 | C2 | semidirect |
| 8. #23757275 | C2 | semidirect |
| 9. #23757270 | C2 | semidirect |
| 10. C2×#19097693 | C2 | semidirect |
| 11. #405×C157 | C2 | semidirect |
| 14. #19097771 | C22 | semidirect |
| 17. #19097763 | C22 | semidirect |
| 26. #19097696 | C22 | semidirect |
| 27. #19097696 | C22 | semidirect |
| 28. #19097696 | C22 | semidirect |
| 33. #19097693 | C22 | semidirect |
| 34. #19097693 | C22 | semidirect |
| 35. #19097693 | C22 | semidirect |
| 39. #97×C157 | C22 | semidirect |
| 40. C4×C8×C157 | C22 | semidirect |
| 135. C157 | #3136 | semidirect |
| 147. #405 | D157 | semidirect |
| 175. #97 | C2×D157 | semidirect |
| 176. C4×C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757901 | 2 |
| #23757842 | 2 |
| #23757638 | 2 |
| #23757633 | 2 |
| #23757628 | 2 |
| #23757620 | 2 |
| #23757279 | 2 |
| #23757275 | 2 |
| #23757270 | 2 |
| C2×#19097693 | 2 |
| #405×C157 | 2 |
| #3136 | 157 |