Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#14578941 | C2 | semidirect |
| 2. C2×#19097778 | C2 | semidirect |
| 4. #23757521 | C2 | semidirect |
| 5. #23757504 | C2 | semidirect |
| 6. #23757309 | C2 | semidirect |
| 7. #23757282 | C2 | semidirect |
| 8. #23757277 | C2 | semidirect |
| 9. #536×C157 | C2 | semidirect |
| 16. C2×#14578938 | C22 | semidirect |
| 18. C22×#11929434 | C22 | semidirect |
| 24. #19097704 | C22 | semidirect |
| 25. #19097702 | C22 | semidirect |
| 26. #19097695 | C22 | semidirect |
| 33. C22⋊Q8×C157 | C22 | semidirect |
| 46. C2×#11929434 | D4 | semidirect |
| 120. C157 | #3057 | semidirect |
| 124. #536 | D157 | semidirect |
| 147. C22⋊Q8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578941 | 2 |
| C2×#19097778 | 2 |
| #23757837 | 2 |
| #23757521 | 2 |
| #23757504 | 2 |
| #23757309 | 2 |
| #23757282 | 2 |
| #23757277 | 2 |
| #536×C157 | 2 |
| #3057 | 157 |