Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
512 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 162 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. #23758222 | C2 | semidirect |
| 15. C2×C4⋊Dic157 | C4 | semidirect |
| 16. C2×#14578933 | C4 | semidirect |
| 17. C2×#14578933 | C4 | semidirect |
| 18. C4⋊C4×D157 | C4 | semidirect |
| 20. C2×C4⋊C4×C157 | C4 | semidirect |
| 96. C157 | #2313 | semidirect |
| 112. C2×C4⋊C4 | #10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758222 | 2 |
| #23758216 | 2 |
| #23758215 | 2 |
| C4×C22⋊#10597845 | 2 |
| C2×C4⋊C4×D157 | 2 |
| #2313 | 157 |