Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19097791 | C2 | semidirect |
| 2. C22×C8×D157 | C2 | semidirect |
| 3. #23757785 | C2 | semidirect |
| 4. #23757780 | C2 | semidirect |
| 5. #23757513 | C2 | semidirect |
| 6. #23757508 | C2 | semidirect |
| 7. #23757505 | C2 | semidirect |
| 8. #23757501 | C2 | semidirect |
| 9. #23757309 | C2 | semidirect |
| 10. #23757270 | C2 | semidirect |
| 11. #416×C157 | C2 | semidirect |
| 15. C2×#14578944 | C22 | semidirect |
| 16. C2×#14578942 | C22 | semidirect |
| 17. C2×#14578941 | C22 | semidirect |
| 18. C2×#14578939 | C22 | semidirect |
| 34. #19097704 | C22 | semidirect |
| 35. #19097702 | C22 | semidirect |
| 36. #19097696 | C22 | semidirect |
| 37. #19097693 | C22 | semidirect |
| 41. #103×C157 | C22 | semidirect |
| 42. #102×C157 | C22 | semidirect |
| 61. C2×#11929434 | D4 | semidirect |
| 133. C2×D157 | #135 | semidirect |
| 148. C157 | #3050 | semidirect |
| 160. #416 | D157 | semidirect |
| 189. #103 | C2×D157 | semidirect |
| 191. #102 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097791 | 2 |
| C22×C8×D157 | 2 |
| #23757785 | 2 |
| #23757780 | 2 |
| #23757513 | 2 |
| #23757508 | 2 |
| #23757505 | 2 |
| #23757501 | 2 |
| #23757309 | 2 |
| #23757270 | 2 |
| #416×C157 | 2 |
| #3050 | 157 |