Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19097730 | C2 | semidirect |
| 2. #23757594 | C2 | semidirect |
| 3. #23757589 | C2 | semidirect |
| 4. #23757584 | C2 | semidirect |
| 5. #23757313 | C2 | semidirect |
| 6. #23757278 | C2 | semidirect |
| 7. #23757237 | C2 | semidirect |
| 13. #19097730 | C22 | semidirect |
| 14. C2×C4⋊Dic157 | C22 | semidirect |
| 15. C2×C4⋊Dic157 | C22 | semidirect |
| 18. #19097704 | C22 | semidirect |
| 19. #19097702 | C22 | semidirect |
| 20. #19097692 | C22 | semidirect |
| 21. #19097692 | C22 | semidirect |
| 22. C22⋊#11929434 | C22 | semidirect |
| 23. C22⋊#11929434 | C22 | semidirect |
| 125. C157 | #3094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097730 | 2 |
| #23757594 | 2 |
| #23757589 | 2 |
| #23757584 | 2 |
| #23757313 | 2 |
| #23757278 | 2 |
| #23757237 | 2 |
| C2×#121×C157 | 2 |
| #3094 | 157 |