Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #23757316 | C2 | semidirect |
| 4. #23757314 | C2 | semidirect |
| 5. #23757308 | C2 | semidirect |
| 6. C2×#19097703 | C2 | semidirect |
| 7. #106×D157 | C2 | semidirect |
| 8. #427×C157 | C2 | semidirect |
| 10. #19097777 | C4 | semidirect |
| 37. #14578938 | C2×C4 | semidirect |
| 38. #14578937 | C2×C4 | semidirect |
| 40. C8×D157 | C2×C4 | semidirect |
| 47. C2×C8×C157 | C2×C4 | semidirect |
| 90. C157 | #2912 | semidirect |
| 97. #427 | D157 | semidirect |
| 133. C2×C8 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097777 | 2 |
| #23757753 | 2 |
| #23757316 | 2 |
| #23757314 | 2 |
| #23757308 | 2 |
| C2×#19097703 | 2 |
| #106×D157 | 2 |
| #427×C157 | 2 |
| #2912 | 157 |