Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
516 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 189 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. #23757124 | C2 | semidirect |
| 6. C42×Dic157 | C2 | semidirect |
| 7. #383×C157 | C2 | semidirect |
| 9. #19097765 | C4 | semidirect |
| 28. #14578933 | C2×C4 | semidirect |
| 37. C42×C157 | C2×C4 | semidirect |
| 68. Dic157 | #126 | semidirect |
| 73. C157 | C4×#126 | semidirect |
| 78. #383 | D157 | semidirect |
| 111. C42 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097765 | 2 |
| #23757162 | 2 |
| #23757155 | 2 |
| #23757124 | 2 |
| #23757120 | 2 |
| C42×Dic157 | 2 |
| #383×C157 | 2 |
| C4×#126 | 157 |