Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
596 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 177 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. #23757173 | C2 | semidirect |
| 3. #23757162 | C2 | semidirect |
| 4. #23757158 | C2 | semidirect |
| 5. #23757151 | C2 | semidirect |
| 6. #23757149 | C2 | semidirect |
| 7. C4×C22⋊Dic157 | C2 | semidirect |
| 8. #23757120 | C2 | semidirect |
| 9. #381×C157 | C2 | semidirect |
| 13. #19097745 | C4 | semidirect |
| 38. C2×C22⋊D157 | C2×C4 | semidirect |
| 45. C4⋊Dic157 | C2×C4 | semidirect |
| 51. #14578931 | C2×C4 | semidirect |
| 58. C22×C4×C157 | C2×C4 | semidirect |
| 134. C157 | #2333 | semidirect |
| 142. #381 | D157 | semidirect |
| 183. C22×C4 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097745 | 2 |
| #23757173 | 2 |
| #23757162 | 2 |
| #23757158 | 2 |
| #23757151 | 2 |
| #23757149 | 2 |
| C4×C22⋊Dic157 | 2 |
| #23757120 | 2 |
| #381×C157 | 2 |
| #2333 | 157 |