Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19097762 | C2 | semidirect |
| 3. #23757575 | C2 | direct (N × H) |
| 4. C2×#19097704 | C2 | semidirect |
| 5. C2×#19097703 | C2 | semidirect |
| 6. C2×#19097700 | C2 | semidirect |
| 12. #19097762 | C22 | semidirect |
| 21. #19097704 | C22 | semidirect |
| 22. #19097703 | C22 | semidirect |
| 23. #19097700 | C22 | semidirect |
| 99. C2×C157 | #478 | semidirect |
| 103. C157 | C2×#478 | semidirect |
| 203. C2 | #23757575 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097762 | 2 |
| C2×D4×Dic157 | 2 |
| #23757575 | 2 |
| C2×#19097704 | 2 |
| C2×#19097703 | 2 |
| C2×#19097700 | 2 |
| C2×#19097692 | 2 |
| C2×#102×C157 | 2 |
| C2×#478 | 157 |