Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
432 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 121 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. C23×#11929434 | C2 | semidirect |
| 3. C2×#19097691 | C2 | semidirect |
| 4. #23757035 | C2 | semidirect |
| 5. #380×C157 | C2 | semidirect |
| 12. #19097745 | C4 | semidirect |
| 32. C2×#11929434 | D4 | semidirect |
| 82. C22×C157 | #102 | semidirect |
| 106. C157 | #1893 | semidirect |
| 111. #380 | D157 | semidirect |
| 194. C22 | #19097691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11929434 | 2 |
| C2×#19097745 | 2 |
| C2×#19097691 | 2 |
| #23757035 | 2 |
| #380×C157 | 2 |
| #1893 | 157 |