Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 2. C22×#14578943 | C2 | semidirect |
| 3. #23757849 | C2 | semidirect |
| 4. #23757747 | C2 | semidirect |
| 5. #23757489 | C2 | semidirect |
| 6. #23757479 | C2 | semidirect |
| 7. #23757283 | C2 | semidirect |
| 8. #23757270 | C2 | semidirect |
| 9. #424×C157 | C2 | semidirect |
| 18. #19097771 | C22 | semidirect |
| 19. #19097759 | C22 | semidirect |
| 26. #19097696 | C22 | semidirect |
| 27. #19097696 | C22 | semidirect |
| 28. #19097693 | C22 | semidirect |
| 32. C4⋊C8×C157 | C22 | semidirect |
| 116. C157 | #3042 | semidirect |
| 124. #424 | D157 | semidirect |
| 146. C4⋊C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097799 | 2 |
| C22×#14578943 | 2 |
| #23757849 | 2 |
| #23757747 | 2 |
| #23757489 | 2 |
| #23757479 | 2 |
| #23757283 | 2 |
| #23757270 | 2 |
| #424×C157 | 2 |
| #3042 | 157 |