Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×C8×Dic157 | C2 | semidirect |
| 5. #23757028 | C2 | semidirect |
| 6. #23757027 | C2 | semidirect |
| 7. C2×C4⋊C8×C157 | C2 | semidirect |
| 40. #14578931 | C8 | semidirect |
| 122. C157 | #1923 | semidirect |
| 124. C2×C4⋊C8 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097683 | 2 |
| C2×C8×Dic157 | 2 |
| C4×#14578931 | 2 |
| #23757028 | 2 |
| #23757027 | 2 |
| C2×C4⋊C8×C157 | 2 |
| #1923 | 157 |