Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
524 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 197 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. #23757155 | C2 | semidirect |
| 4. C4×#14578933 | C2 | semidirect |
| 6. C42×Dic157 | C2 | semidirect |
| 7. #376×C157 | C2 | semidirect |
| 9. #19097728 | C4 | semidirect |
| 75. C157 | #2298 | semidirect |
| 82. #376 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097728 | 2 |
| #23757162 | 2 |
| #23757155 | 2 |
| C4×#14578933 | 2 |
| C4×#14578931 | 2 |
| C42×Dic157 | 2 |
| #376×C157 | 2 |
| #2298 | 157 |