Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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×#19097706 | C2 | semidirect |
| 3. C2×#19097691 | C2 | semidirect |
| 4. C2×#19097687 | C2 | semidirect |
| 5. #23757240 | C2 | semidirect |
| 6. #23757042 | C2 | semidirect |
| 7. #417×C157 | C2 | semidirect |
| 116. C157 | #2051 | semidirect |
| 120. #417 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097796 | 2 |
| C2×#19097706 | 2 |
| C2×#19097691 | 2 |
| C2×#19097687 | 2 |
| #23757240 | 2 |
| #23757042 | 2 |
| #417×C157 | 2 |
| #2051 | 157 |