Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
284 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #23757228 | C2 | semidirect |
| 5. #23757045 | C2 | semidirect |
| 6. #23757043 | C2 | semidirect |
| 7. #405×C157 | C2 | semidirect |
| 15. C2×#14578937 | C4 | semidirect |
| 16. C2×C8×D157 | C4 | semidirect |
| 18. #19097689 | C4 | semidirect |
| 19. #19097687 | C4 | semidirect |
| 106. C157 | #1757 | semidirect |
| 112. #405 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097777 | 2 |
| #23757255 | 2 |
| #23757246 | 2 |
| #23757228 | 2 |
| #23757045 | 2 |
| #23757043 | 2 |
| #405×C157 | 2 |
| #1757 | 157 |