Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#19097729 | C2 | semidirect |
| 3. #23757599 | C2 | direct (N × H) |
| 4. C2×#19097704 | C2 | semidirect |
| 5. C2×#19097693 | C2 | semidirect |
| 6. C2×#19097691 | C2 | semidirect |
| 7. C2×#19097683 | C2 | semidirect |
| 8. C2×#106×C157 | C2 | semidirect |
| 16. #19097729 | C22 | semidirect |
| 21. #19097704 | C22 | semidirect |
| 22. #19097693 | C22 | semidirect |
| 23. #19097691 | C22 | semidirect |
| 24. #19097683 | C22 | semidirect |
| 28. #106×C157 | C22 | semidirect |
| 108. C2×C157 | #482 | semidirect |
| 114. C157 | C2×#482 | semidirect |
| 120. C2×#106 | D157 | semidirect |
| 140. #106 | C2×D157 | semidirect |
| 225. C2 | #23757599 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097746 | 2 |
| C2×#19097729 | 2 |
| #23757599 | 2 |
| C2×#19097704 | 2 |
| C2×#19097693 | 2 |
| C2×#19097691 | 2 |
| C2×#19097683 | 2 |
| C2×#106×C157 | 2 |
| C2×#482 | 157 |