Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C2×#19097802 | C2 | semidirect |
| 3. C4×#14578954 | C2 | semidirect |
| 4. #23757492 | C2 | semidirect |
| 5. #23757485 | C2 | semidirect |
| 6. #23757297 | C2 | semidirect |
| 7. #23757282 | C2 | semidirect |
| 8. #23757278 | C2 | semidirect |
| 9. C2×#124×C157 | C2 | semidirect |
| 13. C2×#14578944 | C22 | semidirect |
| 15. C2×#14578941 | C22 | semidirect |
| 19. C4×Dic314 | C22 | semidirect |
| 20. C4×D628 | C22 | semidirect |
| 25. C4⋊#11929434 | C22 | semidirect |
| 26. #19097695 | C22 | semidirect |
| 125. C157 | #3040 | semidirect |
| 129. C2×#124 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097802 | 2 |
| C2×#19097797 | 2 |
| C4×#14578954 | 2 |
| #23757492 | 2 |
| #23757485 | 2 |
| #23757297 | 2 |
| #23757282 | 2 |
| #23757278 | 2 |
| C2×#124×C157 | 2 |
| #3040 | 157 |