Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
468 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×#19097804 | C2 | semidirect |
| 3. C22×#14578942 | C2 | semidirect |
| 4. C2×#19097779 | C2 | semidirect |
| 5. #23757535 | C2 | direct (N × H) |
| 6. C2×#19097706 | C2 | semidirect |
| 7. C2×#19097689 | C2 | semidirect |
| 8. C2×#100×C157 | C2 | semidirect |
| 12. #19097804 | C22 | semidirect |
| 21. C2×#14578942 | C22 | semidirect |
| 24. #19097779 | C22 | semidirect |
| 29. #19097706 | C22 | semidirect |
| 30. #19097689 | C22 | semidirect |
| 34. #100×C157 | C22 | semidirect |
| 135. C2×C157 | #471 | semidirect |
| 138. C157 | C2×#471 | semidirect |
| 147. C2×#100 | D157 | semidirect |
| 173. #100 | C2×D157 | semidirect |
| 275. C2 | #23757535 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097804 | 2 |
| C2×#19097797 | 2 |
| C22×#14578942 | 2 |
| C2×#19097779 | 2 |
| #23757535 | 2 |
| C2×#19097706 | 2 |
| C2×#19097689 | 2 |
| C2×#100×C157 | 2 |
| C2×#471 | 157 |