Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 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. C2×#19097790 | C2 | semidirect |
| 2. C22×C8×D157 | C2 | semidirect |
| 3. #23757783 | C2 | semidirect |
| 4. #23757515 | C2 | semidirect |
| 5. #23757514 | C2 | semidirect |
| 6. #23757506 | C2 | semidirect |
| 7. #23757501 | C2 | semidirect |
| 8. #23757500 | C2 | semidirect |
| 9. #23757310 | C2 | semidirect |
| 10. #23757266 | C2 | semidirect |
| 11. #466×C157 | C2 | semidirect |
| 15. C2×Dic628 | C22 | semidirect |
| 16. C2×#14578942 | C22 | semidirect |
| 31. #19097705 | C22 | semidirect |
| 32. #19097702 | C22 | semidirect |
| 33. #19097696 | C22 | semidirect |
| 34. #19097694 | C22 | semidirect |
| 35. #19097692 | C22 | semidirect |
| 36. C2×D8×C157 | C22 | semidirect |
| 39. #107×C157 | C22 | semidirect |
| 40. #102×C157 | C22 | semidirect |
| 63. C8×D157 | D4 | semidirect |
| 121. C22×C157 | #135 | semidirect |
| 129. C2×D157 | #135 | semidirect |
| 145. C157 | #3050 | semidirect |
| 153. #466 | D157 | semidirect |
| 163. C2×D8 | C2×D157 | semidirect |
| 181. #107 | C2×D157 | semidirect |
| 186. #102 | C2×D157 | semidirect |
| 274. C22 | #19097790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097790 | 2 |
| C22×C8×D157 | 2 |
| #23757783 | 2 |
| #23757515 | 2 |
| #23757514 | 2 |
| #23757506 | 2 |
| #23757501 | 2 |
| #23757500 | 2 |
| #23757310 | 2 |
| #23757266 | 2 |
| #466×C157 | 2 |
| #3050 | 157 |