Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23757282 | C2 | semidirect |
| 5. #23757034 | C2 | semidirect |
| 6. #23757032 | C2 | semidirect |
| 7. #419×C157 | C2 | semidirect |
| 11. #19097760 | C4 | semidirect |
| 42. C4×Dic157 | C2×C4 | semidirect |
| 48. C2×Q8×C157 | C2×C4 | semidirect |
| 107. C157 | #1885 | semidirect |
| 112. #419 | D157 | semidirect |
| 138. C2×Q8 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097760 | 2 |
| #23757747 | 2 |
| #23757282 | 2 |
| C2×#19097687 | 2 |
| #23757034 | 2 |
| #23757032 | 2 |
| #419×C157 | 2 |
| #1885 | 157 |