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×#19097804 | C2 | semidirect |
| 3. C2×#19097759 | C2 | semidirect |
| 4. C4×#14578954 | C2 | semidirect |
| 5. #23757496 | C2 | semidirect |
| 6. #23757489 | C2 | semidirect |
| 7. #23757283 | C2 | semidirect |
| 8. #23757279 | C2 | semidirect |
| 9. #423×C157 | C2 | semidirect |
| 15. C2×Dic628 | C22 | semidirect |
| 17. C2×#14578943 | C22 | semidirect |
| 22. C4×Dic314 | C22 | semidirect |
| 23. C4×D628 | C22 | semidirect |
| 29. #19097696 | C22 | semidirect |
| 34. C4⋊C8×C157 | C22 | semidirect |
| 125. C157 | #3040 | semidirect |
| 133. #423 | D157 | semidirect |
| 158. C4⋊C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097804 | 2 |
| C2×#19097799 | 2 |
| C2×#19097759 | 2 |
| C4×#14578954 | 2 |
| #23757496 | 2 |
| #23757489 | 2 |
| #23757283 | 2 |
| #23757279 | 2 |
| #423×C157 | 2 |
| #3040 | 157 |