Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#19097694 | C2 | semidirect |
| 4. #23757035 | C2 | semidirect |
| 9. #19097750 | C4 | semidirect |
| 23. C2×Dic314 | C2×C4 | semidirect |
| 30. C4⋊Dic157 | C2×C4 | semidirect |
| 83. C22×C157 | #103 | semidirect |
| 105. C157 | #1872 | semidirect |
| 189. C22 | #19097694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097750 | 2 |
| C2×#19097694 | 2 |
| C2×C22⋊#11929434 | 2 |
| #23757035 | 2 |
| C22×C4⋊C4×C157 | 2 |
| #1872 | 157 |