Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
336 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19097681 | C2 | semidirect |
| 4. C2×C8×Dic157 | C2 | semidirect |
| 5. #23757027 | C2 | semidirect |
| 6. #23757027 | C2 | semidirect |
| 16. C22⋊#11929434 | C4 | semidirect |
| 22. C22⋊C8×C157 | C4 | semidirect |
| 104. C157 | #1750 | semidirect |
| 125. C22⋊C8 | Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097730 | 2 |
| C2×C22⋊#11929434 | 2 |
| C2×#19097681 | 2 |
| C2×C8×Dic157 | 2 |
| #23757027 | 2 |
| C2×C22⋊C8×C157 | 2 |
| #1750 | 157 |