Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. #23757823 | C2 | semidirect |
| 2. C2×C4×D628 | C2 | semidirect |
| 3. #23757587 | C2 | semidirect |
| 4. #23757554 | C2 | semidirect |
| 5. #23757469 | C2 | semidirect |
| 6. #23757409 | C2 | semidirect |
| 7. C4×D1256 | C2 | semidirect |
| 8. #431×C157 | C2 | semidirect |
| 13. #19097771 | C22 | semidirect |
| 14. #19097768 | C22 | semidirect |
| 23. C4×D628 | C22 | semidirect |
| 26. #19097705 | C22 | semidirect |
| 28. #19097693 | C22 | semidirect |
| 30. C4⋊C8×C157 | C22 | semidirect |
| 32. C4×C8×C157 | C22 | semidirect |
| 76. D628 | #41 | semidirect |
| 87. C2×C4×C157 | D8 | semidirect |
| 120. C157 | #3100 | semidirect |
| 129. #431 | D157 | semidirect |
| 149. C4⋊C8 | C2×D157 | semidirect |
| 153. C4×C8 | C2×D157 | semidirect |
| 208. C2×C4 | D1256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757823 | 2 |
| C2×C4×D628 | 2 |
| #23757587 | 2 |
| #23757554 | 2 |
| #23757469 | 2 |
| #23757409 | 2 |
| C4×D1256 | 2 |
| #431×C157 | 2 |
| #3100 | 157 |