Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #23757170 | C2 | semidirect |
| 6. #23757143 | C2 | semidirect |
| 7. #23757142 | C2 | semidirect |
| 8. #23757138 | C2 | semidirect |
| 9. #382×C157 | C2 | semidirect |
| 13. #19097728 | C4 | semidirect |
| 45. #14578933 | C2×C4 | semidirect |
| 49. C4×Dic157 | C2×C4 | semidirect |
| 56. C42×C157 | C2×C4 | semidirect |
| 73. C4×D157 | C4⋊C4 | semidirect |
| 109. C157 | #2317 | semidirect |
| 119. #382 | D157 | semidirect |
| 166. C42 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097729 | 2 |
| C2×#19097728 | 2 |
| C2×C4⋊C4×D157 | 2 |
| #23757170 | 2 |
| #23757147 | 2 |
| #23757143 | 2 |
| #23757142 | 2 |
| #23757138 | 2 |
| #382×C157 | 2 |
| #2317 | 157 |