Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#19097819 | C2 | semidirect |
| 2. #23758073 | C2 | semidirect |
| 3. #23757847 | C2 | semidirect |
| 4. #23757458 | C2 | semidirect |
| 5. #23757448 | C2 | semidirect |
| 6. #23757289 | C2 | semidirect |
| 7. C2×#101×C157 | C2 | semidirect |
| 17. #19097804 | C22 | semidirect |
| 19. #19097799 | C22 | semidirect |
| 21. #19097769 | C22 | semidirect |
| 22. #19097760 | C22 | semidirect |
| 26. #19097697 | C22 | semidirect |
| 29. #101×C157 | C22 | semidirect |
| 123. C157 | #3020 | semidirect |
| 131. C2×#101 | D157 | semidirect |
| 153. #101 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097819 | 2 |
| #23758073 | 2 |
| #23757847 | 2 |
| #23757458 | 2 |
| #23757448 | 2 |
| #23757289 | 2 |
| C2×#101×C157 | 2 |
| #3020 | 157 |