Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C2×#19097797 | C2 | semidirect |
| 2. #23757840 | C2 | semidirect |
| 3. #23757748 | C2 | semidirect |
| 4. #23757486 | C2 | semidirect |
| 5. #23757466 | C2 | semidirect |
| 6. #23757299 | C2 | semidirect |
| 7. #23757278 | C2 | semidirect |
| 8. #23757270 | C2 | semidirect |
| 9. C22×D8×C157 | C2 | semidirect |
| 12. C2×#14578942 | C22 | semidirect |
| 13. C2×#14578939 | C22 | semidirect |
| 15. #19097767 | C22 | semidirect |
| 16. #19097758 | C22 | semidirect |
| 20. D4×Dic157 | C22 | semidirect |
| 24. #19097700 | C22 | semidirect |
| 25. #19097696 | C22 | semidirect |
| 26. #19097693 | C22 | semidirect |
| 27. #19097692 | C22 | semidirect |
| 60. C2×D4×C157 | D4 | semidirect |
| 121. C157 | #3041 | semidirect |
| 124. C22×D8 | D157 | semidirect |
| 168. C2×D4 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097797 | 2 |
| #23757840 | 2 |
| #23757748 | 2 |
| #23757486 | 2 |
| #23757466 | 2 |
| #23757299 | 2 |
| #23757278 | 2 |
| #23757270 | 2 |
| C22×D8×C157 | 2 |
| #3041 | 157 |