Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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×#19097778 | C2 | semidirect |
| 2. #23757756 | C2 | semidirect |
| 3. #23757278 | C2 | semidirect |
| 4. #23757274 | C2 | semidirect |
| 5. #23757269 | C2 | semidirect |
| 6. C2×#19097692 | C2 | semidirect |
| 9. C2×#14578938 | C22 | semidirect |
| 10. C22×#11929434 | C22 | semidirect |
| 13. #19097730 | C22 | semidirect |
| 14. C2×C4⋊Dic157 | C22 | semidirect |
| 15. #19097695 | C22 | semidirect |
| 16. #19097695 | C22 | semidirect |
| 17. #19097692 | C22 | semidirect |
| 18. #19097692 | C22 | semidirect |
| 19. #19097692 | C22 | semidirect |
| 21. H(5,𝔽2)×C157 | C4 | semidirect |
| 41. #41×C157 | C2×C4 | semidirect |
| 49. C2×D4×C157 | C2×C4 | semidirect |
| 97. C157 | #2897 | semidirect |
| 107. H(5,𝔽2) | Dic157 | semidirect |
| 129. #41 | C2×Dic157 | semidirect |
| 137. C2×D4 | C2×Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097778 | 2 |
| #23757756 | 2 |
| #23757278 | 2 |
| #23757274 | 2 |
| #23757269 | 2 |
| C2×#19097692 | 2 |
| C2×H(5,𝔽2)×C157 | 2 |
| #2897 | 157 |